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Jorge Olivares-Vinales

Publications and source records attributed to Jorge Olivares-Vinales.

5 recordsLinked to original sources
arXiv2026

Absolutely continuous invariant measures and the Collet-Eckmann condition for long-branched Sturmian unimodal maps

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 stunted Lorenz construction of Anušić, Bruin, and Činč, and their quadratic representatives with the maps constructed by Blé from rigid rotations. We compute the cutting and co-cutting times explicitly and establish criteria for the existence and nonexistence of absolutely continuous invariant probability measures. We also show that, for Lebesgue-almost every rotation angle, no finite-order $S$-unimodal realization satisfies the Collet-Eckmann condition.

math.DS↗
arXiv2026

Towers and Bratteli-Vershik systems in Fibonacci-like unimodal maps

For a class of Fibonacci-like unimodal maps, the restriction to the $ω$-limit set of the unique turning point defines a minimal Cantor system. We construct these Cantor sets geometrically using a nested sequence of finite covers with a tower structure. From this tower structure, we recover the associated Bratteli-Vershik model determined by the cutting times and obtain an explicit formula for the unique ergodic invariant probability measure supported on the $ω$-limit set. We conclude with applications illustrating the scope of the construction.

math.DS↗
arXiv2024

The Artin-Mazur zeta function for interval maps

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 gave a characterization for the rationality of the Artin-Mazur zeta function in terms of the orbit of the unique turning point. We show that for multimodal maps, the previous characterization does not hold.

math.DS↗
arXiv2021

Invariant measures for interval maps without Lyapunov exponents

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 is not defined. This map has a Lorenz-like singularity and non-flat critical points.

math.DS↗