Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
COCYCLES OVER PARTIALLY HYPERBOLIC MAPS ARTUR AVILA, JIMMY SANTAMARIA, MARCELO VIANA
 

Summary: COCYCLES OVER PARTIALLY HYPERBOLIC MAPS
ARTUR AVILA, JIMMY SANTAMARIA, MARCELO VIANA
Abstract. We give a general necessary condition for the extremal (largest and
smallest) Lyapunov exponents of a H¨older continuous cocycle over a volume
preserving partially hyperbolic diffeomorphism to coincide. This condition
applies to smooth cocycles, with linear and projective cocycles as special cases.
It is based on an abstract rigidity result for fiber bundle sections that are
holonomy-invariant, or even just continuous, over the strong-stable leaves and
the strong-unstable leaves of the diffeomorphism. As an application, we prove
that the subset of H¨older continuous linear cocycles for which the extremal
Lyapunov exponents do coincide is meager and even has infinite codimension.
Contents
1. Introduction 2
2. Partially hyperbolic diffeomorphisms 6
3. Linear cocycles: fiber bunching and holonomies 8
4. Smooth cocycles: domination and holonomies 15
5. Invariant measures of smooth cocycles 17
6. Density points 22
7. Bi-essential invariance implies essential bi-invariance 27
8. Accessibility and continuity 35

  

Source: Avila, Artur - Instituto Nacional de Matemática Pura e Aplicada (IMPA)

 

Collections: Mathematics