scholarly journals Uniform hyperbolicity of invariant cylinder

2017 ◽  
Vol 106 (1) ◽  
pp. 1-43 ◽  
Author(s):  
Chong-Qing Cheng
Keyword(s):  
Uniform Hyperbolicity

scholarly journals Kupka–Smale diffeomorphisms at the boundary of uniform hyperbolicity: a model

Nonlinearity ◽  
2017 ◽  
Vol 30 (10) ◽  
pp. 3895-3931
Author(s):  
Renaud Leplaideur ◽  
Isabel Lugão Rios
Keyword(s):  
Uniform Hyperbolicity

scholarly journals Equilibrium measures for the Hénon map at the first bifurcation: uniqueness and geometric/statistical properties

2014 ◽  
Vol 36 (1) ◽  
pp. 215-255 ◽  
Author(s):  
SAMUEL SENTI ◽  
HIROKI TAKAHASI
Keyword(s):  
Existence And Uniqueness ◽  
Thermodynamic Formalism ◽  
Invariant Probability Measure ◽  
Statistical Properties ◽  
Limit Set ◽  
Bifurcation Parameter ◽  
Large Interval ◽  
Equilibrium Measures ◽  
Uniform Hyperbolicity ◽  
Unstable Direction

For strongly dissipative Hénon maps at the first bifurcation parameter where the uniform hyperbolicity is destroyed by the formation of tangencies inside the limit set, we establish a thermodynamic formalism, i.e. we prove the existence and uniqueness of an invariant probability measure that minimizes the free energy associated with a non-continuous geometric potential$-t\log J^{u}$, where$t\in \mathbb{R}$is in a certain large interval and$J^{u}$denotes the Jacobian in the unstable direction. We obtain geometric and statistical properties of these measures.

scholarly journals Pointwise hyperbolicity implies uniform hyperbolicity

2014 ◽  
Vol 34 (7) ◽  
pp. 2819-2827 ◽  
Author(s):  
Boris Hasselblatt ◽  
◽  
Yakov Pesin ◽  
Jörg Schmeling ◽  
◽  
...  
Keyword(s):  
Uniform Hyperbolicity

Uniform Hyperbolicity on Random Sets

Sankhya A ◽  
2018 ◽  
Vol 81 (2) ◽  
pp. 387-398
Author(s):  
Abbas Ali Rashid ◽  
Alireza Zamani Bahabadi
Keyword(s):  
Random Sets ◽  
Uniform Hyperbolicity

scholarly journals Large deviation principles for non-uniformly hyperbolic rational maps

2010 ◽  
Vol 31 (2) ◽  
pp. 321-349 ◽  
Author(s):  
HENRI COMMAN ◽  
JUAN RIVERA-LETELIER
Keyword(s):  
Large Deviation ◽  
Periodic Points ◽  
Rational Maps ◽  
Pressure Function ◽  
Hölder Continuous ◽  
Large Deviation Principles ◽  
Continuous Potential ◽  
Uniform Hyperbolicity ◽  
Level 2 ◽  
Unique Equilibrium State

AbstractWe show some level-2 large deviation principles for rational maps satisfying a strong form of non-uniform hyperbolicity, called ‘Topological Collet–Eckmann’. More precisely, we prove a large deviation principle for the distribution of iterated preimages, periodic points, and Birkhoff averages. For this purpose we show that each Hölder continuous potential admits a unique equilibrium state, and that the pressure function can be characterized in terms of iterated preimages, periodic points, and Birkhoff averages. Then we use a variant of a general result of Kifer.

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