Generalization of geometric Poincaré theorem for small perturbations
type: Item
instance of: scholarly article
title: Generalization of geometric Poincaré theorem for small perturbations
zbMATH Open document ID: 0959.37047
author: E. A. Kudryavtseva
published in: Regular and Chaotic Dynamics
publication date: 1999-11-08T00:00:00Z
review text: The number of periodic orbits is estimated which persist under a \(C^2\)-smooth perturbation of a Hamiltonian system containing in a level of the Hamiltonian a smooth closed submanifold \(\Lambda\) filled with periodic orbits. It is supposed that the fibration \(\Lambda\) into closed orbits is a smooth bundle with a smooth base \(B\) and \(S^1\) as the fiber. The estimate is given for two cases: i) the bundle is trivial; ii) \(B\) can carry a locally flat Riemannian metric. The estimate of the number of periodic orbits is given via the number of critical points of a smooth function on \(B\). Results obtained are refinement of those proved before by \textit{A. Weinstein} [Math. Z. 159, 235-248 (1978; Zbl 0376.58008), Ann. Math. (2) 98, 377-410 (1973; Zbl 0271.58008)].
Mathematics Subject Classification ID: 37J40
Mathematics Subject Classification ID: 37J45
Mathematics Subject Classification ID: 58E05
zbMATH DE Number: 1281657
zbMATH Keywords: periodic orbit
zbMATH Keywords: Hamiltonian
zbMATH Keywords: family
zbMATH Keywords: perturbation
zbMATH Keywords: fibration
zbMATH Keywords: persistence
zbMATH Keywords: Morse theory
reviewed by: L. M. Lerman
MaRDI profile type: Publication
DOI: 10.1070/RD1998V003N02ABEH000070
description: scientific article; zbMATH DE number 1281657