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Partially hyperbolic dynamics in dimension three

Published online by Cambridge University Press:  09 May 2017

PABLO D. CARRASCO ,
FEDERICO RODRIGUEZ-HERTZ ,
JANA RODRIGUEZ-HERTZ  and
RAÚL URES
PABLO D. CARRASCO
Affiliation:
ICMC-USP, Avenida Trabalhador São-carlense 400, São Carlos, SP 13566-590, Brazil email pdcarrasco@gmail.com
FEDERICO RODRIGUEZ-HERTZ
Affiliation:
PSU Mathematics Department, University Park, State College, PA 16802, USA email hertz@math.psu.edu
JANA RODRIGUEZ-HERTZ
Affiliation:
IMERL-FING, Julio Herrera y Reissig 565, Montevideo 11300, Uruguay email jana@fing.edu.uy, ures@fing.edu.uy
RAÚL URES
Affiliation:
IMERL-FING, Julio Herrera y Reissig 565, Montevideo 11300, Uruguay email jana@fing.edu.uy, ures@fing.edu.uy
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Abstract

Partial hyperbolicity appeared in the 1960s as a natural generalization of hyperbolicity. In the last 20 years, there has been great activity in this area. Here we survey the state of the art in some related topics, focusing especially on partial hyperbolicity in dimension three. 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 the dynamics in revealing ways.

Type
Survey Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 8 , December 2018 , pp. 2801 - 2837
Copyright
© Cambridge University Press, 2017 

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