5 papers
Absolutely continuous invariant measures and the Collet-Eckmann condition for long-branched Sturmian unimodal maps
Jorge Olivares-Vinales
We study long-branched unimodal maps for which the sequence of values of the kneading map form a Sturmian word. We identify these kneading classes with those arising from the stunt…
Towers and Bratteli-Vershik systems in Fibonacci-like unimodal maps
Jorge Olivares-Vinales, Semin Yoo
For a class of Fibonacci-like unimodal maps, the restriction to the -limit set of the unique turning point defines a minimal Cantor system. We construct these Cantor sets geomet…
Non-existence of wandering intervals for asymmetric unimodal maps
Jorge Olivares-Vinales, Weixiao Shen
We prove that an asymmetric unimodal map has no wandering intervals.
The Artin-Mazur zeta function for interval maps
Jorge Olivares-Vinales
In this work we study the Artin-Mazur zeta function for piecewise monotone functions acting on a compact interval of real numbers. In the case of unimodal maps, Milnor and Thurston…
Invariant measures for interval maps without Lyapunov exponents
Jorge Olivares-Vinales
We construct an invariant measure for a piecewise analytic interval map whose Lyapunov exponent is not defined. Moreover, for a set of full measure, the pointwise Lyapunov exponent…