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Theorem 2 of A. Kercheval, Denjoy minimal sets are far from affine, Ergodic Theory and Dynamical Systems 22 (2002), 1803-1812 is corrected by adding a C^2 bound to the hypotheses.
Mary Rees has constructed a minimal homeomorphism of the 2-torus with positive topological entropy. This homeomorphism f is obtained by enriching the dynamics of an irrational rotation R. We improve Rees construction, allowing to start with any homeo
We show that the horocycle flows of open tight hyperbolic surfaces do not admit minimal sets.
We develop a technique, pseudo-suspension, that applies to invariant sets of homeomorphisms of a class of annulus homeomorphisms we describe, Handel-Anosov-Katok (HAK) homeomorphisms, that generalize the homeomorphism first described by Handel. Given
In this paper we compute the dimension of a class of dynamically defined non-conformal sets. Let $Xsubseteqmathbb{T}^2$ denote a Bedford-McMullen set and $T:Xto X$ the natural expanding toral endomorphism which leaves $X$ invariant. For an open set $
We show that every (invertible, or noninvertible) minimal Cantor system embeds in $mathbb{R}$ with vanishing derivative everywhere. We also study relations between local shrinking and periodic points.