31/10 --16h00 - 16h50
Choquard Problems in R^N Interacting with the Negative Part of the Spectrum (Auditório 207 - Pavilhão de Auditórios)
Olímpio Hiroshi Miyagaki (UFSCar)
31/10 --16h50 - 17h40
Fractal dimensions of hyperbolic graphs and horseshoes (Auditório 207 - Pavilhão de Auditórios)
Deberton Moura de Oliveira (UFMG)
Fractal Geometry is a field of Mathematics under development, which is open for expansion and new insights. Moreover, fractals are objects that arouses curiosity, since these objects have unorthodox properties, an irregular geometry and some self-similarities. On the other hand, since it is an area in development, there are some distinct fractal dimension calculations for hyperbolic graphs, as we are going to present here, based on two papers. The first one calculates the Hausdorff dimension of a horseshoe using its intersection with the unstable manifold, with a strong usage of ergodic theory and hyperbolic dynamics. However, the second one, calculates the box dimension of an attractor by almost periodic functions and Fourier series, with a bit of hyperbolic dynamics.
31/10 -- 17h40 - 18h30
On the generic behavior of the metric entropy, and related quantities, of uniformly continuous maps over Polish metric spaces (Auditório 207 - Pavilhão de Auditórios)
Silas Luiz de Carvalho (UFMG)
We show that if f is a uniformly continuous map defined over a Polish metric space, then the set of f-invariant measures with zero metric entropy is a G_\delta set (in the weak topology). In particular, this set is generic if the set of f-periodic measures is dense in the set of f-invariant measures. This settles a conjecture posed by Sigmund (Sigmund, K. On dynamical systems with the specification property. Trans. Amer. Math. Soc. 190 (1974), 285-299) which states that the metric entropy of an invariant measure of a topological dynamical system that satisfies the periodic specification property is typically zero.