Partially hyperbolic dynamics in dimension 3

Abstract

Partial hyperbolicity appeared in the sixties as a natural generaliza- tion of hyperbolicity. In the last 20 years in this area there has been great activity. Here we survey the state of the art in some topics, focusing especially in partial hyperbolicity in dimension 3. The reason for this is not only that it is the smallest dimension in which non-degenerate partial hyperbolicity can occur, but also that the topology of 3-manifolds influences this dynamics in revealing ways.

Updated version, to appear in Ergodic Theory and Dynamical Systems

References in corpus (3)

• Seifert Fibered Spaces: Notes for a course given in the Spring of 1993
• A non-dynamically coherent example on ${\mathbb{T}}^3$
• On the geometry of horseshoes in higher dimensions

Cited by in corpus (4)

• Partial hyperbolicity and classification: a survey
• Surgery for partially hyperbolic dynamical systems I. Blow-ups of invariant submanifolds
• Partially hyperbolic diffeomorphisms homotopic to the identity on 3-manifolds
• Partially hyperbolic diffeomorphisms with one-dimensional neutral center on 3-manifolds