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Equi-topological entropy curves for skew tent maps in the square
Abstract We consider skew tent maps Tα, β(x) such that (α,β)∈[0,1]2 is the turning point of TTα, β, that is, Tα, β = βα $\begin{array}{} \frac{{\beta}}{{\alpha}} \end{array} $x for 0≤ x ≤ α and Tα,…
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On co-σ-porosity of the parameters with dense critical orbits for skew tent maps and matching on generalized β-transformations
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Convergence of ergodic averages for many group rotations
Suppose that $G$ is a compact Abelian topological group, $m$ is the Haar measure on $G$ and $f:G\rightarrow \mathbb{R}$ is a measurable function. Given $(n_{k})$ , a strictly monotone increasing…
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On co-$\sigma$-porosity of the parameters with dense critical orbits for skew tent maps and matching on generalized $\beta$-transformations
We prove that the critical point and the point 1 have dense orbits for Lebesgue-a.e., parameter pairs in the two-parameter skew-tent family and generalised β-transformations. As an application, we…
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Isentropes, Lyapunov exponents and Ergodic averages
Isentropes and Lyapunov exponents
TLDR
This paper provides an efficient new method of finding the value of the Lyapunov exponent of these maps by using the slope of the tangent to the isentrope of skew tent maps.
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