Stable topological non-conjugacy of Hamiltonian systems on two-dimensional surfaces
type: Item
instance of: scholarly article
title: Stable topological non-conjugacy of Hamiltonian systems on two-dimensional surfaces
zbMATH Open document ID: 0979.37024
author: Yu. A. Brailov
author: E. A. Kudryavtseva
published in: Moscow University Mathematics Bulletin
publication date: 2000-10-31T00:00:00Z
review text: The regular Morse functions are studied on two-dimensional surfaces. These functions possess the property of stability in the following sense. Two Hamiltonian systems are stable topologically non-conjugated near the saddle critical levels, if (1) these Hamiltonian systems are not topologically conjugated in any arbitrary small neighborhoods \(U_1\) and \(U_2\) of saddle levels; (2) for any arbitrary small perturbations of the functions \(F_1\) and \(F_2\) and the si mplectic structures \(\omega_1\) and \(\omega_2\) the perturbed systems remain topologically non-conjugated in any domains \(\tilde U_1\) and \(\tilde U_2\) containing \(U_1\) and \(U_2\) respectively. The authors describe the natural subclass in the set of all such Morse functions.
Mathematics Subject Classification ID: 37J05
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 37B99
zbMATH DE Number: 1524038
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: topological non-conjugation
zbMATH Keywords: Morse functions
MaRDI profile type: Publication
Recommended article: Stable conjugation invariants of Hamiltonian systems on two-dimensional surfaces
Recommended article: A criterion for the topological conjugacy of Hamiltonian flows on two-dimensional compact surfaces
Recommended article: Topological classification of Hamiltonian systems on two-dimensional noncompact manifolds
Recommended article: Exact topological classification of Hamiltonian flows on smooth two-dimensional surfaces
Recommended article: Topological methods in the instability problem of Hamiltonian systems
Recommended article: HAMILTONIAN SYSTEMS WITH POSITIVE TOPOLOGICAL ENTROPY AND CONJUGATE POINTS
Recommended article: The classification of Hamiltonian systems on two-dimensional surfaces
Recommended article: Nikolai Ivanovich Lobachevskii (on the bicentenary of his birth)
Recommended article: ON TYPICAL TOPOLOGICAL PROPERTIES OF INTEGRABLE HAMILTONIAN SYSTEMS
Recommended article: Q3791929
description: scientific article; zbMATH DE number 1524038