Uniform Hyperbolicity on Random Sets

Abbas Ali Rashid () and Alireza Zamani Bahabadi ()
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Abbas Ali Rashid: Ferdowsi University of Mashhad
Alireza Zamani Bahabadi: Ferdowsi University of Mashhad

Sankhya A: The Indian Journal of Statistics, 2019, vol. 81, issue 2, No 5, 387-398

Abstract: Abstract Let Λ be a random compact invariant (with respect to a random map) set with a uniform tangent bundle splitting. We show that if there is a random non-uniformly hyperbolic variable x0 on Λ and the space of limit points of time averages of random Dirac measures on the orbit of x0 coincides with the space of invariant probability measures supported on Λ then, Λ is a random uniformly hyperbolic set.

Keywords: Random hyperbolicity; Uniform tangent bundle splitting; Random non-uniformly hyperbolic; Primary 47A55; Secondary 39B52; 34K20; 39B82. (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13171-018-0146-6

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