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2004, Volume 11, Issue 2&3: 615-619. Doi: 10.3934/dcds.2004.11.615
This issue Previous Article Sharkovsky orderings of higher order difference equations Next Article Symbolic dynamics from signed matrices

A note on periodic orbits for singular-hyperbolic flows

  • 1.

    Instituto de Matemàtica, Universidade Federal do Rio de Janeiro, C. P. 68530, CEP 21945-970, Rio de Janeiro

Received:  May 2003
Revised:  February 2004
Published:  September 2004
Abstract Related Papers Cited by
    Abstract
  • A singular-hyperbolic set for flows is a partially hyperbolic set with singularities (hyperbolic ones) and volume expanding central direction [7]. Several properties of hyperbolic systems have been conjectured for the singular-hyperbolic sets [8, p. 335]. Related to these conjectures we shall prove the existence of transitive, isolated, singular-hyperbolic set without periodic orbits on any $3$-manifold. In particular, the periodic orbits are not necessarily dense in the limit set of a isolated singular-hyperbolic set.
    Mathematics Subject Classification: Primary: 37D30; Secondary: 37C27.

    Citation:
    shu

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