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- W3103644350 abstract "We consider a family of skew-products of the form $(Tx, g_x(t)) : X times mathbb{R} to X times mathbb{R}$ where $T$ is a continuous expanding Markov map and $g_x : mathbb{R} to mathbb{R}$ is a family of homeomorphisms of $mathbb{R}$. A function $u: X to mathbb{R}$ is said to be an invariant graph if $mathrm{graph}(u) = {(x,u(x)) mid xin X}$ is an invariant set for the skew-product; equivalently if $u(T(x)) = g_x(u(x))$. A well-studied problem is to consider the existence, regularity and dimension-theoretic properties of such functions, usually under strong contraction or expansion conditions (in terms of Lyapunov exponents or partial hyperbolicity) in the fibre direction. Here we consider such problems in a setting where the Lyapunov exponent in the fibre direction is zero on a set of periodic orbits. We prove that $u$ either has the structure of a `quasi-graph' (or `bony graph') or is as smooth as the dynamics, and we give a criteria for this to happen." @default.
- W3103644350 created "2020-11-23" @default.
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- W3103644350 date "2018-05-01" @default.
- W3103644350 modified "2023-10-18" @default.
- W3103644350 title "Invariant graphs of a family of non-uniformly expanding skew products over Markov maps" @default.
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- W3103644350 doi "https://doi.org/10.1088/1361-6544/aab596" @default.
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