Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T04:01:42.828Z Has data issue: false hasContentIssue false
  • English
  • Français

Gradient-like flows on high-dimensional manifolds

Published online by Cambridge University Press:  02 April 2001

R. N. CRUZ  and
K. A. DE REZENDE
R. N. CRUZ
Affiliation:
Departamento de Matemática, Universidade Estadual de Campinas, 13083-970 Campinas, São Paulo, Brazil (e-mail: [email protected], [email protected])
K. A. DE REZENDE
Affiliation:
Departamento de Matemática, Universidade Estadual de Campinas, 13083-970 Campinas, São Paulo, Brazil (e-mail: [email protected], [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

The main purpose of this paper is to study the implications that the homology index of critical sets of smooth flows on closed manifolds M have on both the homology of level sets of M and the homology of M itself. The bookkeeping of the data containing the critical set information of the flow and topological information of M is done through the use of Lyapunov graphs. Our main result characterizes the necessary conditions that a Lyapunov graph must possess in order to be associated to a Morse–Smale flow. With additional restrictions on an abstract Lyapunov graph L we determine sufficient conditions for L to be associated to a flow on M.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 2 , April 1999 , pp. 339 - 362
Copyright
1999 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)