A note on periodic orbits for singular-hyperbolic flows
Carlos Arnoldo Morales - Instituto de Matemàtica, Universidade Federal do Rio de Janeiro, C. P. 68530, CEP 21945-970, Rio de Janeiro, Brazil (email)
Abstract: A singular-hyperbolic set for flows is a partially hyperbolic set with singularities (hyperbolic ones) and volume expanding central direction . 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.
Keywords: Flow, periodic orbit, partially hyperbolic set.
Received: May 2003; Revised: February 2004; Available Online: June 2004.
2015 Impact Factor1.127