Fractional embeddings and stochastic time (2008)
Cresson, Jacky, Inizan, Pierre
As a model problem for the study of chaotic Hamiltonian systems, we look for the effects of a long-tail distribution of recurrence times on a fixed Hamiltonian dynamics. We follow Stanislavsky's...
Fractional embeddings and stochastic time (2008)
Cresson, Jacky, Inizan, Pierre
As a model problem for the study of chaotic Hamiltonian systems, we look for the effects of a long-tail distribution of recurrence times on a fixed Hamiltonian dynamics. We follow Stanislavsky's...
Fractional embeddings and stochastic time (2008)
Cresson, Jacky, Inizan, Pierre
As a model problem for the study of chaotic Hamiltonian systems, we look for the effects of a long-tail distribution of recurrence times on a fixed Hamiltonian dynamics. We follow Stanislavsky's...
Constants of Motion for Non-Differentiable Quantum Variational Problems (2008)
Cresson, Jacky, Frederico, Gastao S. F., Torres, Delfim F. M.
We extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the scale relativity theory setting. Both Lagrangian and Hamiltonian versions of Noether's theorem are...
Mould Calculus for Hamiltonian Vector Fields (2008)
Cresson, Jacky, Morin, Guillaume
We present the general framework of \'Ecalle's moulds in the case of linearization of a formal vector field without and within resonances. We enlighten the power of moulds by their universality, and...
Mould Calculus for Hamiltonian Vector Fields (2008)
Cresson, Jacky, Morin, Guillaume
We present the general framework of Écalle's moulds in the case of linearization of a formal vector field without and within resonances. We enlighten the power of moulds by their universality, and...
Mould Calculus for Hamiltonian Vector Fields (2008)
Cresson, Jacky, Morin, Guillaume
We present the general framework of Écalle's moulds in the case of linearization of a formal vector field without and within resonances. We enlighten the power of moulds by their universality, and...
On the first integral conjecture of Rene Thom (2007)
Cresson, Jacky, Daniilidis, Aris, Shiota, Masahiro
More that half a century ago R. Thom asserted in an unpublished manuscript that, generically, vector fields on compact connected smooth manifolds without boundary can admit only trivial continuous...
On the first integral conjecture of Rene Thom (2007)
Cresson, Jacky, Daniilidis, Aris, Shiota, Masahiro
More that half a century ago R. Thom asserted in an unpublished manuscript that, generically, vector fields on compact connected smooth manifolds without boundary can admit only trivial continuous...
On the first integral conjecture of Rene Thom (2007)
Cresson, Jacky, Daniilidis, Aris, Shiota, Masahiro
More that half a century ago R. Thom asserted in an unpublished manuscript that, generically, vector fields on compact connected smooth manifolds without boundary can admit only trivial continuous...
Phénomènes de symétrie dans des formes linéaires en polyzêtas (2007)
Cresson, Jacky, Fischler, Stephane, Rivoal, Tanguy
We give two generalizations, in arbitrary depth, of the symmetry phenomenon used by Ball-Rivoal to prove that infinitely many values of Riemann $\zeta$ function at odd integers are irrational. These...
Phénomènes de symétrie dans des formes linéaires en polyzêtas (2007)
Cresson, Jacky, Fischler, Stephane, Rivoal, Tanguy
We give two generalizations, in arbitrary depth, of the symmetry phenomenon used by Ball-Rivoal to prove that infinitely many values of Riemann $\zeta$ function at odd integers are irrational. These...
Séries hypergéométriques multiples et polyzêtas (2006)
Cresson, Jacky, Fischler, Stephane, Rivoal, Tanguy
We describe a theoretical and effective algorithm which enables us to prove that rather general hypergeometric series and integrals can be decomposed as linear combinations of multiple zeta values,...
S\'eries hyperg\'eom\'etriques multiples et polyz\^etas (2006)
Cresson, Jacky, Fischler, Stephane, Rivoal, Tanguy
We describe a theoretical and effective algorithm which enables us to prove that rather general hypergeometric series and integrals can be decomposed as linear combinations of multiple zeta values,...
Ph\'{e}nom\`{e}nes de sym\'{e}trie dans des formes lin\'{e}aires en polyz\^{e}tas (2006)
Cresson, Jacky, Fischler, Stephane, Rivoal, Tanguy
We give two generalizations, in arbitrary depth, of the symmetry phenomenon used by Ball-Rivoal to prove that infinitely many values of Riemann $\zeta$ function at odd integers are irrational. These...
Séries hypergéométriques multiples et polyzêtas (2006)
Cresson, Jacky, Fischler, Stephane, Rivoal, Tanguy
We describe a theoretical and effective algorithm which enables us to prove that rather general hypergeometric series and integrals can be decomposed as linear combinations of multiple zeta values,...
Phénomènes de symétrie dans des formes linéaires en polyzêtas (2006)
Cresson, Jacky, Fischler, Stephane, Rivoal, Tanguy
We give two generalizations, in arbitrary depth, of the symmetry phenomenon used by Ball-Rivoal to prove that infinitely many values of Riemann $\zeta$ function at odd integers are irrational. These...
Séries hypergéométriques multiples et polyzêtas (2006)
Cresson, Jacky, Fischler, Stephane, Rivoal, Tanguy
We describe a theoretical and effective algorithm which enables us to prove that rather general hypergeometric series and integrals can be decomposed as linear combinations of multiple zeta values,...
Phénomènes de symétrie dans des formes linéaires en polyzêtas (2006)
Cresson, Jacky, Fischler, Stephane, Rivoal, Tanguy
We give two generalizations, in arbitrary depth, of the symmetry phenomenon used by Ball-Rivoal to prove that infinitely many values of Riemann $\zeta$ function at odd integers are irrational. These...
Séries hypergéométriques multiples et polyzêtas (2006)
Cresson, Jacky, Fischler, Stephane, Rivoal, Tanguy
We describe a theoretical and effective algorithm which enables us to prove that rather general hypergeometric series and integrals can be decomposed as linear combinations of multiple zeta values,...
Phénomènes de symétrie dans des formes linéaires en polyzêtas (2006)
Cresson, Jacky, Fischler, Stephane, Rivoal, Tanguy
We give two generalizations, in arbitrary depth, of the symmetry phenomenon used by Ball-Rivoal to prove that infinitely many values of Riemann $\zeta$ function at odd integers are irrational. These...
Fractional embedding of differential operators and Lagrangian systems (2006)
This paper is a contribution to the general program of embedding theories of dynamical systems. Following our previous work on the Stochastic embedding theory developed with S. Darses, we define the...
Fractional embedding of differential operators and Lagrangian systems (2006)
This paper is a contribution to the general program of embedding theories of dynamical systems. Following our previous work on the Stochastic embedding theory developed with S. Darses, we define the...
Fractional embedding of differential operators and Lagrangian systems (2006)
This paper is a contribution to the general program of embedding theories of dynamical systems. Following our previous work on the Stochastic embedding theory developed with S. Darses, we define the...
Fractional embedding of differential operators and Lagrangian systems (2006)
This paper is a contribution to the general program of embedding theories of dynamical systems. Following our previous work on the Stochastic embedding theory developed with S. Darses, we define the...
Fractional embedding of differential operators and Lagrangian systems (2006)
This paper is a contribution to the general program of embedding theories of dynamical systems. Following our previous work on the Stochastic embedding theory developed with S. Darses, we define the...
About the Trimmed and the Poincare-Dulac normal form of diffeomorphisms (2006)
Cresson, Jacky, Raissy, Jasmin
We study two particular continuous prenormal forms as defined by Jean Ecalle and Bruno Vallet for local analytic diffeomorphism: the Trimmed form and the Poincare-Dulac normal form. We first give a...
About the Trimmed and the Poincare-Dulac normal form of diffeomorphisms (2006)
Cresson, Jacky, Raissy, Jasmin
We study two particular continuous prenormal forms as defined by Jean Ecalle and Bruno Vallet for local analytic diffeomorphism: the Trimmed form and the Poincare-Dulac normal form. We first give a...
About the Trimmed and the Poincare-Dulac normal form of diffeomorphisms (2006)
Cresson, Jacky, Raissy, Jasmin
We study two particular continuous prenormal forms as defined by Jean Ecalle and Bruno Vallet for local analytic diffeomorphism: the Trimmed form and the Poincare-Dulac normal form. We first give a...
About the Trimmed and the Poincare-Dulac normal form of diffeomorphisms (2006)
Cresson, Jacky, Raissy, Jasmin
We study two particular continuous prenormal forms as defined by Jean Ecalle and Bruno Vallet for local analytic diffeomorphism: the Trimmed form and the Poincare-Dulac normal form. We first give a...
About the Trimmed and the Poincare-Dulac normal form of diffeomorphisms (2006)
Cresson, Jacky, Raissy, Jasmin
We study two particular continuous prenormal forms as defined by Jean Ecalle and Bruno Vallet for local analytic diffeomorphism: the Trimmed form and the Poincare-Dulac normal form. We first give a...
Hyperbolicity versus partial-hyperbolicity and the transversality-torsion phenomenon (2006)
Cresson, Jacky, Guillet, Christophe
In this paper, we describe a process to create hyperbolicity in the neighbourhood of a homoclinic orbit to a partially hyperbolic torus for three degrees of freedom Hamiltonian systems: the...
Hyperbolicity versus partial-hyperbolicity and the transversality-torsion phenomenon (2006)
Cresson, Jacky, Guillet, Christophe
In this paper, we describe a process to create hyperbolicity in the neighbourhood of a homoclinic orbit to a partially hyperbolic torus for three degrees of freedom Hamiltonian systems: the...
Hyperbolicity versus partial-hyperbolicity and the transversality-torsion phenomenon (2006)
Cresson, Jacky, Guillet, Christophe
In this paper, we describe a process to create hyperbolicity in the neighbourhood of a homoclinic orbit to a partially hyperbolic torus for three degrees of freedom Hamiltonian systems: the...
Hyperbolicity versus partial-hyperbolicity and the transversality-torsion phenomenon (2006)
Cresson, Jacky, Guillet, Christophe
In this paper, we describe a process to create hyperbolicity in the neighbourhood of a homoclinic orbit to a partially hyperbolic torus for three degrees of freedom Hamiltonian systems: the...
Hyperboliity versus partial-hyperbolicity and the transversality-torsion phenomenon (2006)
Cresson, Jacky, Guillet, Christophe
In this paper, we describe a process to create hyperbolicity in the neighbourhood of a homoclinic orbit to a partially hyperbolic torus for three degrres of freedom Hamiltonian systems: the...
Lemme de coherence et théorème de Noether stochastique (2005)
Cresson, Jacky, Darses, Sébastien
The stochastic embedding procedure associates a stochastic Euler-Lagrange equation (SEL) to the standard Euler-Lagrange equation (EL). Can we derive (SEL) from a generalized least action principle?...
Plongement stochastique des systèmes lagrangiens (2005)
Cresson, Jacky, Darses, Sébastien
We define an operator which extends classical differentiation from smooth deterministic functions to certain stochastic processes. Based on this operator, we define a procedure which associates a...
Lemme de coherence et théorème de Noether stochastique (2005)
Cresson, Jacky, Darses, Sébastien
The stochastic embedding procedure associates a stochastic Euler-Lagrange equation (SEL) to the standard Euler-Lagrange equation (EL). Can we derive (SEL) from a generalized least action principle?...
Plongement stochastique des systèmes lagrangiens (2005)
Cresson, Jacky, Darses, Sébastien
We define an operator which extends classical differentiation from smooth deterministic functions to certain stochastic processes. Based on this operator, we define a procedure which associates a...
Lemme de coherence et théorème de Noether stochastique (2005)
Cresson, Jacky, Darses, Sébastien
The stochastic embedding procedure associates a stochastic Euler-Lagrange equation (SEL) to the standard Euler-Lagrange equation (EL). Can we derive (SEL) from a generalized least action principle?...
Plongement stochastique des systèmes lagrangiens (2005)
Cresson, Jacky, Darses, Sébastien
We define an operator which extends classical differentiation from smooth deterministic functions to certain stochastic processes. Based on this operator, we define a procedure which associates a...
Plongement stochastique des syst\`{e}mes lagrangiens (2005)
Cresson, Jacky, Darses, Sébastien
We define an operator which extends classical differentiation from smooth deterministic functions to certain stochastic processes. Based on this operator, we define a procedure which associates a...
Lemme de coherence et th\'{e}or\`{e}me de Noether stochastique (2005)
Cresson, Jacky, Darses, Sébastien
The stochastic embedding procedure associates a stochastic Euler-Lagrange equation (SEL) to the standard Euler-Lagrange equation (EL). Can we derive (SEL) from a generalized least action principle?...
Lemme de coherence et théorème de Noether stochastique (2005)
Cresson, Jacky, Darses, Sébastien
The stochastic embedding procedure associates a stochastic Euler-Lagrange equation (SEL) to the standard Euler-Lagrange equation (EL). Can we derive (SEL) from a generalized least action principle?...
Plongement stochastique des systèmes lagrangiens (2005)
Cresson, Jacky, Darses, Sébastien
We define an operator which extends classical differentiation from smooth deterministic functions to certain stochastic processes. Based on this operator, we define a procedure which associates a...
A lambda-lemma for normally hyperbolic invariant manifolds (2005)
Cresson, Jacky, Wiggins, Stephen
Let $N$ be a smooth manifold and $f:N\rightarrow N$ be a $C^l$, $l\geq 2$ diffeomorphism. Let $M$ be a normally hyperbolic invariant manifold, not necessarily compact. We prove an analogue of the...
A lambda-lemma for normally hyperbolic invariant manifolds (2005)
Cresson, Jacky, Wiggins, Stephen
Let $N$ be a smooth manifold and $f:N\to N$ be a $C^l$, $l\geq 2$ diffeomorphism. Let $M$ be a normally hyperbolic invariant manifold, not necessarily compact. We prove an analogue of the...
A lambda-lemma for normally hyperbolic invariant manifolds (2005)
Cresson, Jacky, Wiggins, Stephen
Let $N$ be a smooth manifold and $f:N\rightarrow N$ be a $C^l$, $l\geq 2$ diffeomorphism. Let $M$ be a normally hyperbolic invariant manifold, not necessarily compact. We prove an analogue of the...
A lambda-lemma for normally hyperbolic invariant manifolds (2005)
Cresson, Jacky, Wiggins, Stephen
Let $N$ be a smooth manifold and $f:N\rightarrow N$ be a $C^l$, $l\geq 2$ diffeomorphism. Let $M$ be a normally hyperbolic invariant manifold, not necessarily compact. We prove an analogue of the...
A lambda-lemma for normally hyperbolic invariant manifolds (2005)
Cresson, Jacky, Wiggins, Stephen
Let $N$ be a smooth manifold and $f:N\rightarrow N$ be a $C^l$, $l\geq 2$ diffeomorphism. Let $M$ be a normally hyperbolic invariant manifold, not necessarily compact. We prove an analogue of the...
Stochastic embedding of dynamical systems (2005)
Cresson, Jacky, Darses, Sébastien
Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics. In some cases, for example when studying the long term behaviour...
Stochastic embedding of dynamical systems (2005)
Cresson, Jacky, Darses, Sébastien
Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics. In some cases, for example when studying the long term behaviour...
Stochastic embedding of dynamical systems (2005)
Cresson, Jacky, Darses, Sébastien
Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics. In some cases, for example when studying the long term behaviour...
Stochastic embedding of dynamical systems (2005)
Cresson, Jacky, Darses, Sébastien
Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics. In some cases, for example when studying the long term behaviour...
Stochastic embedding of dynamical systems (2005)
Cresson, Jacky, Darses, Sébastien
Most physical systems are modelled by an ordinary or a partial differential equation, like the n-body problem in celestial mechanics. In some cases, for example when studying the long term behaviour...
This paper is an introduction to mould calculus as introduced by Jean Ecalle. We give a precise definition of moulds and describe there main properties. We translate mould symmetries (alterna(e)l and...
About analytic non integrability (2005)
We prove several general results on non existence of analytic first integrals for analytic diffeomorphisms possessing a hyperbolic fixed point.
Dynamique des nombres et physique des oscillateurs (2005)
We consider the superheterodyning system discovered by Armstrong and Schottky in 1924. This system is the basic piece of any communication system. We prove that the frequency spectrum of this system...
Dynamique des nombres et physique des oscillateurs (2005)
We consider the superheterodyning system discovered by Armstrong and Schottky in 1924. This system is the basic piece of any communication system. We prove that the frequency spectrum of this system...
About analytic non integrability (2005)
We prove several general results on non existence of analytic first integrals for analytic diffeomorphisms possessing a hyperbolic fixed point.
This paper is an introduction to mould calculus as introduced by Jean Ecalle. We give a precise definition of moulds and describe there main properties. We translate mould symmetries (alterna(e)l and...
This paper is an introduction to mould calculus as introduced by Jean Ecalle. We give a precise definition of moulds and describe there main properties. We translate mould symmetries (alterna(e)l and...
About analytic non integrability (2005)
We prove several general results on non existence of analytic first integrals for analytic diffeomorphisms possessing a hyperbolic fixed point.
Dynamique des nombres et physique des oscillateurs (2005)
We consider the superheterodyning system discovered by Armstrong and Schottky in 1924. This system is the basic piece of any communication system. We prove that the frequency spectrum of this system...
This paper is an introduction to mould calculus as introduced by Jean Ecalle. We give a precise definition of moulds and describe there main properties. We translate mould symmetries (alterna(e)l and...
About analytic non integrability (2005)
We prove several general results on non existence of analytic first integrals for analytic diffeomorphisms possessing a hyperbolic fixed point.
Dynamique des nombres et physique des oscillateurs (2005)
We consider the superheterodyning system discovered by Armstrong and Schottky in 1924. This system is the basic piece of any communication system. We prove that the frequency spectrum of this system...
This paper is an introduction to mould calculus as introduced by Jean Ecalle. We give a precise definition of moulds and describe there main properties. We translate mould symmetries (alterna(e)l and...
About analytic non integrability (2005)
We prove several general results on non existence of analytic first integrals for analytic diffeomorphisms possessing a hyperbolic fixed point.
Dynamique des nombres et physique des oscillateurs (2005)
We consider the superheterodyning system discovered by Armstrong and Schottky in 1924. This system is the basic piece of any communication system. We prove that the frequency spectrum of this system...
Non-differentiable variational principles (2004)
We develop a calculus of variations for functionals which are defined on a set of non differentiable curves. We first extend the classical differential calculus in a quantum calculus, which allows us...
Scale calculus and the Schrodinger equation (2002)
We introduce the scale calculus, which generalizes the classical differential calculus to non differentiable functions. The new derivative is called the scale difference operator. We also introduce...