Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems
type: Item
instance of: scholarly article
title: Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems
zbMATH Open document ID: 0941.37021
DOI: 10.1016/S0167-2789(97)00173-5
author: Stephen Wiggins
author: Misha Rudnev
published in: Physica D
publication date: 2000-02-01T00:00:00Z
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 37C55
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 70H05
zbMATH DE Number: 1397354
zbMATH Keywords: Arnold diffusion
zbMATH Keywords: exponentially small splitting of separatrices
zbMATH Keywords: a priori stable systems
zbMATH Keywords: KAM theory
zbMATH Keywords: homoclinic manifolds
zbMATH Keywords: weakly hyperbolic tori
zbMATH Keywords: Nekhoroshev exponent
zbMATH Keywords: Melnikov integrals
zbMATH Keywords: analytic perturbation
zbMATH Keywords: homoclinic orbits
zbMATH Keywords: whiskered tori
MaRDI profile type: Publication
cites work: Q5508817
cites work: A proof of Nekhoroshev's theorem for the stability times in nearly integrable Hamiltonian systems
cites work: Stability of motions near resonances in quasi-integrable Hamiltonian systems
cites work: Perturbation d'un hamiltonien partiellement hyperbolique
cites work: An approach to arnold's diffusion through the calculus of variations
cites work: Q4285310
cites work: Exponentially small splitting of separatrices under fast quasiperiodic forcing
cites work: An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum
cites work: Q3968495
cites work: Q4378706
cites work: Biasymptotic solutions of perturbed integrable Hamiltonian systems
cites work: Transcendentally small transversality in the rapidly forced pendulum
cites work: TWISTLESS KAM TORI, QUASI FLAT HOMOCLINIC INTERSECTIONS, AND OTHER CANCELLATIONS IN THE PERTURBATION SERIES OF CERTAIN COMPLETELY INTEGRABLE HAMILTONIAN SYSTEMS: A REVIEW
cites work: Q4287414
cites work: A proof of existence of whiskered tori with quasi flat homoclinic intersections in a class of almost integrable hamiltonian systems
cites work: Q4203852
cites work: Splitting of separatrices for standard and semistandard mappings
cites work: Complex analysis and convolution operators
cites work: Q4514089
cites work: Q4893081
cites work: The analytic invariants of an area-preserving mapping near a hyperbolic fixed point
cites work: AN EXPONENTIAL ESTIMATE OF THE TIME OF STABILITY OF NEARLY-INTEGRABLE HAMILTONIAN SYSTEMS
cites work: Integrability of hamiltonian systems on cantor sets
cites work: Nekhoroshev estimates for quasi-convex Hamiltonian systems
cites work: KAM theory near multiplicity one resonant surfaces in perturbations of a-priori stable Hamiltonian systems
cites work: Q3310704
cites work: THE MECHANISM OF DESTRUCTION OF RESONANCE TORI OF HAMILTONIAN SYSTEMS
cites work: Global bifurcations and chaos. Analytical methods
cites work: On the conservation of hyperbolic invariant tori for Hamiltonian systems
full work available at URL: s0167-2789(97)00173-5
OpenAlex ID: W2064274015
Recommended article: Erratum to ``Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems''
Recommended article: Exponentially small splitting of separatrices for whiskered tori in Hamiltonian systems
Recommended article: Exponentially small splitting for whiskered tori in Hamiltonian systems: continuation of transverse homoclinic orbits
Recommended article: Exponentially small splitting for whiskered tori in Hamiltonian systems: Flow-box coordinates and upper bounds
Recommended article: A proof of existence of whiskered tori with quasi flat homoclinic intersections in a class of almost integrable hamiltonian systems
Recommended article: Exponentially small splitting of separatrices for perturbed integrable standard-like maps
Recommended article: Q5461246
Recommended article: Q4203852
Recommended article: Q4407888
Recommended article: Exponentially small splitting of separatrices and transversality associated to whiskered tori with quadratic frequency ratio
description: scientific article; zbMATH DE number 1397354