Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-24T18:39:39.880Z Has data issue: false hasContentIssue false
  • English
  • Français

Lyapunov graph continuation

Published online by Cambridge University Press:  16 January 2003

M. A. BERTOLIM ,
M. P. MELLO  and
K. A. DE REZENDE
M. A. BERTOLIM
Affiliation:
Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, SP, Brazil
M. P. MELLO
Affiliation:
Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, Campinas, SP, Brazil (e-mail: [email protected])
K. A. DE REZENDE
Affiliation:
Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, Campinas, SP, Brazil (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper the Poincaré–Hopf inequalities are shown to be necessary and sufficient conditions for an abstract Lyapunov graph L to be continued to an abstract Lyapunov graph of Morse type. The Lyapunov graphs considered may represent smooth flows on closed orientable n-manifolds, n \geq 2. The continuation which is presented by means of a constructive algorithm, is shown to be unique in dimensions two and three. In all other dimensions, the exact number of possible continuations of L are presented.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 1 , February 2003 , pp. 1 - 58
Copyright
2003 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.)