Now showing items 1-20 of 24

• #### A methodology for obtaining asymptotic estimates for the exponentially small splitting of separatrices to whiskered tori with quadratic frequencies ﻿

(2014-07)
External research report
Open Access
• #### Continuation of the exponentially small lower bounds for the splitting of separatrices to a whiskered torus with silver ratio ﻿

(2014-09)
External research report
Open Access
We study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly-integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We consider ...
• #### Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio ﻿

(Springer, 2014-11)
Article
Open Access
We study the exponentially small splitting of invariant manifolds of whiskered (hyperbolic) tori with two fast frequencies in nearly integrable Hamiltonian systems whose hyperbolic part is given by a pendulum. We ...
• #### Effective stability and KAM theory ﻿

(1995)
Article
Open Access
The two main stability results for nearly integrable Hamiltonian systems are revisited: Nekhoroshev theorem, concerning exponential lower bounds for the stability time (effective stability), and KAM theorem, concerning ...
• #### Estimates on invariant tori near an elliptic equilibrium point of a Hamiltonian system ﻿

(1996)
Article
Open Access
We give a precise statement for KAM theorem in a neighbourhood of an elliptic equilibrium point of a Hamiltonian system. If the frequencies of the elliptic point are nonresonant up to a certain order $K\ge4$, and a ...
• #### Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tori with quadratic and cubic frequencies ﻿

(2013)
External research report
Open Access
We study the splitting of invariant manifolds of whiskered t ori with two or three frequencies in nearly-integrable Hamiltonian systems. We consider 2-dimensional tori with a frequency vector ω = (1 , Ω) where Ω is ...
• #### Exponentially small asymptotic estimates for the splitting of separatrices to whiskered tort with quadratic and cubic frequencies ﻿

(2014-01-01)
Article
Open Access
We study the splitting of invariant manifolds of whiskered tori with two or three frequencies in nearly-integrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a 2-dimensional torus ...
• #### Exponentially small estimates for KAM theorem near an elliptic equilibrium point ﻿

(1997)
Article
Open Access
We give a precise statement of KAM theorem for a Hamiltonian system in a neighborhood of an elliptic equilibrium point. If the frequencies of the elliptic point satisfy a Diophantine condition, with exponent $\tau$, and ...
• #### Exponentially small lower bounds for the splitting of separatrices to whiskered tori with frequencies of constant type ﻿

(2014-02)
External research report
Open Access
We study the splitting of invariant manifolds of whiskered tori with two frequencies in nearlyintegrable Hamiltonian systems, such that the hyperbolic part is given by a pendulum. We consider a 2-dimensional torus with ...
• #### Exponentially small splitting for whiskered tori in Hamiltonian systems: Continuation of transverse homoclinic orbits ﻿

(2003)
Article
Open Access
We consider an example of singular or weakly hyperbolic Hamiltonian, with 3 degrees of freedom, as a model for the behaviour of a nearly-integrable Hamiltonian near a simple resonance. The model consists of an integrable ...
• #### Exponentially small splitting for whiskered tori in Hamiltonian systems: Flow-box coordinates and upper bounds ﻿

(2003)
Article
Open Access
We consider a singular or weakly hyperbolic Hamiltonian, with $n+1$ degrees of freedom, as a model for the behaviour of a nearly-integrable Hamiltonian near a simple resonance. The model consists of an integrable Hamiltonian ...
• #### Exponentially small splitting of separatrices and transversality associated to whiskered tori with quadratic frequency ratio ﻿

(2016-06)
Article
Open Access
The splitting of invariant manifolds of whiskered (hyperbolic) tori with two frequencies in a nearly integrable Hamiltonian system, whose hyperbolic part is given by a pendulum, is studied. We consider a torus with a fast ...
• #### Exponentially small splitting of separatrices and transversality associated to whiskered tori with quadratic frequency ratio ﻿

(2015)
External research report
Open Access
The splitting of invariant manifolds of whiskered (hyperbolic) tori with two frequencies in a nearly-integrable Hamiltonian system, whose hyperbolic part is given by a pendulum, is studied.
• #### Exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies ﻿

(2020-01-01)
Article
Open Access
We study the splitting of invariant manifolds of whiskered (hyperbolic) tori with three frequencies in a nearly-integrable Hamiltonian system, whose hyperbolic part is given by a pendulum. We consider a 3-dimensional torus ...
• #### Exponentially small splitting of separatrices associated to 3D whiskered tori with cubic frequencies ﻿

(2019-06)
External research report
Open Access
We study the splitting of invariant manifolds of whiskered (hyperbolic) tori with three frequencies in a nearly-integrable Hamiltonian system, whose hyperbolic part is given by a pendulum. We consider a 3-dimensional ...
• #### Exponentially small splitting of separatrices for whiskered tori in Hamiltonian systems ﻿

(2003)
Article
Open Access
We study the existence of transverse homoclinic orbits in a singular or weakly hyperbolic Hamiltonian, with $3$ degrees of freedom, as a model for the behaviour of a nearly-integrable Hamiltonian near a simple resonance. ...
• #### Homoclinic orbits to invariant tori in Hamiltonian systems ﻿

(1998)
Article
Open Access
We consider a perturbation of an integrable Hamiltonian system which possesses invariant tori with coincident whiskers (like some rotators and a pendulum). Our goal is to measure the splitting distance between the perturbed ...
• #### Homoclinic orbits to invariant tori near a homoclinic orbit to center-center-saddle equilibrium ﻿

(2003)
Article
Open Access
We consider a perturbation of an integrable Hamiltonian vector field with three degrees of freedom with a center–center–saddle equilibrium having a homoclinic orbit or loop. With the help of a Poincaré map (chosen based ...
• #### Splitting and melnikov potentials in hamiltonian systems ﻿

(2000)
Article
Open Access
• #### Splitting potential and Poincaré-Melnikov method for whiskered tori in Hamiltonian Systems ﻿

(1999)
Article
Open Access
We deal with a perturbation of a hyperbolic integrable Hamiltonian system with n+1 degrees of freedom. The integrable system is assumed to have n-dimensional hyperbolic invariant tori with coincident whiskers (separatric ...