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Carlos Gustavo Tamm de Araujo Moreira

Publications and source records attributed to Carlos Gustavo Tamm de Araujo Moreira.

4 recordsLinked to original sources
arXiv2026

Dynamical spectra for skew products with unit circle fiber

The dynamical Markov and Lagrange spectra are subsets of the real line widely studied and that share some similarities with the classical spectra, e.g. typical dynamical spectra, associated to horseshoes with Hausdorff dimension greater than one, have nonempty interior and, in the conservative setting, the intersections of the spectra with half-lines determine a continuous function. Here we study some similar questions in the context of skew products of surface diffeomorphisms with unit circle fiber.

math.DS↗
arXiv2017

Dynamical Systems, Fractal Geometry and Diophantine Approximations

We describe in this survey several results relating Fractal Geometry, Dynamical Systems and Diophantine Approximations, including a description of recent results related to geometrical properties of the classical Markov and Lagrange spectra and generalizations in Dynamical Systems and Differential Geometry.

math.DS↗
arXiv2012

On the geometry of horseshoes in higher dimensions

The criterion of the recurrent compact set was introduced by Moreira and Yoccoz to prove that stable intersections of regular Cantor sets on the real line are dense in the region where the sum of their Hausdorff dimensions is bigger than 1. We adapt this concept to the context of horseshoes in ambient dimension higher than 2 and prove that horseshoes with upper stable dimension bigger than 1 satisfy, typically and persistently, the adapted criterion of the recurrent compact set. As consequences we show some persistent geometric properties of these horseshoes. In particular, typically and persistently, horseshoes with upper stable dimension bigger than 1 present blenders.

math.DS↗