Welcome to the website of the research group on dynamic systems at IMECC. Our main purpose is to integrate the different research groups interested in investigating geometric and topological aspects of dynamical phenomena within the Mathematics Institute of Unicamp.
Speaker: Sebastian Burgos (Penn State University)Abstract: We study the set of irregular points for Birkhoff averages for a class of topologically mixing subshifts of finite type. It is well known that, despite the irregular set having zero measure for every invariant measure, it possesses full topological entropy and Hausdorff dimension. We establish that for these systems, the…
Speaker: Neemias MartinsAbstract: In this talk, we present a symbolic dynamical system defined in a locally invertible context and show how its folding and Kolmogorov-Sinai entropies are related. We use these results to study the isomorphism problem of extended Bernoulli maps following Ornstein’s techniques.Date: 12/11/2024 – 16:00Room: 321 IMECC
Speaker: Matheus CunhasAbstract: We show that the hyperbolicity of a linear delay-difference equation with infinite delay, expressed in terms of the existence of an exponential dichotomy, can be completely characterized by the hyperbolicity of a linear cocycle obtained from the solutions of the equation. As an appli-cation of this characterization, we obtain several consequences: the…
Speaker: Matheus CunhaAbstract: The concept of sliding Shilnikov connection has been recently introduced and represents an important notion in Filippov systems, because its existence implies chaotic behavior on an invariant subset of the system. The investigation of its properties has just begun, and understanding the topology and complexity of its invariant set is of interest.…
Speaker: Matias ZimmermannAbstract: The main purpose of this short seminar is to present and popularize the notion of a Random Dynamical System (RDS) and to give an impression of its scope. The concept of a RSD is an extension of the deterministic concept of a dynamical system, and it reduces to the latter if it…
Speaker: Paulo Lupatini Abstract: We prove that the specification property implies infinite topological entropy for operators acting on infinite dimensional $F$-spaces. We also prove that compact operators acting on Banach spaces have finite entropy and the entropy depends exclusively on the operators point spectrum. Additionally, we prove that the variational principle is not valid for compact operators…