scholarly journals Markov extensions for dynamical systems with holes: An application to expanding maps of the interval

2005 ◽  
Vol 146 (1) ◽  
pp. 189-221 ◽  
Author(s):  
Mark F. Demers
Keyword(s):  
Dynamical Systems ◽  
Expanding Maps ◽  
Markov Extensions

scholarly journals Inducing schemes for multi-dimensional piecewise expanding maps

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Peyman Eslami
Keyword(s):  
Dynamical Systems ◽  
Statistical Properties ◽  
Expanding Maps ◽  
Return Times ◽  
Return Map ◽  
Exponential Tails ◽  
Inducing Schemes ◽  
Piecewise Expanding Maps

<p style='text-indent:20px;'>We construct inducing schemes for general multi-dimensional piecewise expanding maps where the base transformation is Gibbs-Markov and the return times have exponential tails. Such structures are a crucial tool in proving statistical properties of dynamical systems with some hyperbolicity. As an application we check the conditions for the first return map of a class of multi-dimensional non-Markov, non-conformal intermittent maps.</p>

Invariant rigid geometric structures and expanding maps

2011 ◽  
Vol 32 (3) ◽  
pp. 941-959 ◽  
Author(s):  
YONG FANG
Keyword(s):  
Dynamical Systems ◽  
Geometric Structure ◽  
Closed Manifold ◽  
Expanding Maps ◽  
Geometric Structures ◽  
Global Rigidity ◽  
Chaotic Dynamical Systems ◽  
Expanding Map ◽  
Locally Homogeneous ◽  
Rigid Geometric Structures

AbstractIn the first part of this paper, we consider several natural problems about locally homogeneous rigid geometric structures. In particular, we formulate a notion of topological completeness which is adapted to the study of global rigidity of chaotic dynamical systems. In the second part of the paper, we prove the following result: let φ be a C∞ expanding map of a closed manifold. If φ preserves a topologically complete C∞ rigid geometric structure, then φ is C∞ conjugate to an expanding infra-nilendomorphism.

Coupled-expanding maps and one-sided symbolic dynamical systems

2009 ◽  
Vol 39 (5) ◽  
pp. 2138-2149 ◽  
Author(s):  
Yuming Shi ◽  
Hyonhui Ju ◽  
Guanrong Chen
Keyword(s):  
Dynamical Systems ◽  
Expanding Maps
Sign in / Sign up

Export Citation Format

Share Document