scholarly journals Exponential mixing for skew products with discontinuities

2016 ◽  
Vol 369 (2) ◽  
pp. 783-803 ◽  
Author(s):  
Oliver Butterley ◽  
Peyman Eslami
Keyword(s):  
Exponential Mixing ◽  
Skew Products

scholarly journals Stretched-exponential mixing for skew products with discontinuities

2015 ◽  
Vol 37 (1) ◽  
pp. 146-175 ◽  
Author(s):  
PEYMAN ESLAMI
Keyword(s):  
Constant Function ◽  
Piecewise Constant Function ◽  
Exponential Rate ◽  
Skew Product ◽  
Piecewise Constant ◽  
Exponential Mixing ◽  
Stretched Exponential ◽  
Skew Products ◽  
Expanding Map

Consider the skew product $F:\mathbb{T}^{2}\rightarrow \mathbb{T}^{2}$, $F(x,y)=(f(x),y+\unicode[STIX]{x1D70F}(x))$, where $f:\mathbb{T}^{1}\rightarrow \mathbb{T}^{1}$ is a piecewise $\mathscr{C}^{1+\unicode[STIX]{x1D6FC}}$ expanding map on a countable partition and $\unicode[STIX]{x1D70F}:\mathbb{T}^{1}\rightarrow \mathbb{R}$ is piecewise $\mathscr{C}^{1}$. It is shown that if $\unicode[STIX]{x1D70F}$ is not Lipschitz-cohomologous to a piecewise constant function on the joint partition of $f$ and $\unicode[STIX]{x1D70F}$, then $F$ is mixing at a stretched-exponential rate.

Topological entropy of piecewise bimonotone skew products

2009 ◽  
Vol 15 (1) ◽  
pp. 53-69
Author(s):  
Franz Hofbauer ◽  
Peter Maličký ◽  
L'ubomír Snoha
Keyword(s):  
Topological Entropy ◽  
Skew Products
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