Arnold's diffusion in isochronous systems
type: Item
instance of: scholarly article
title: Arnold's diffusion in isochronous systems
zbMATH Open document ID: 0936.37031
DOI: 10.1023/A:1009893118532
published in: Mathematical Physics, Analysis and Geometry
publication date: 2000-05-22T00:00:00Z
review text: In the paper the following family of Hamiltonian systems with three degrees of freedom \[ H=\omega A_{0} + \frac{I^{2}}{2}+g^{2}(\cos \varphi -1) + \varepsilon f(\varphi, \alpha), \] where \( \varphi\in T^{1}\), \(\alpha\in T^{2}\), \(I\in \mathbb{R}\), \(A_{0}\in \mathbb{R}^{2},\) is investigated. Following a non-variational approach developed by \textit{L. Chierchia} and the author in [Ann. Inst. Henri Poincaré B, Phys. Théor. 60, 1-144 (1994)] the existence of diffusion in this system is shown. Moreover, after adding a new idea of elastic heteroclinic chain, the author improves the related estimates for the diffusion time in the ``isochronous'' cases considered in the paper. This bound is conceptually independent from the other works.
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 34D23
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 70H09
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 70H14
zbMATH DE Number: 1334574
zbMATH Keywords: Arnold's diffusion
zbMATH Keywords: homoclinic splitting
zbMATH Keywords: KAM
zbMATH Keywords: Hamiltonian systems with three degrees of freedom
zbMATH Keywords: heteroclinic chain
author: G. Gallavotti
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1334574