O DMat parabeniza o aluno Daniel Roizman de Vasconcellos pela defesa de dissertação de mestrado realizada no dia 13 de abril de 2026.

Title: Transfer operator, correlation dimension and the shortest distance between orbits

Abstract: This dissertation investigates the statistical properties of dynamical systems, focusing on the asymptotic behavior of the shortest distance between orbits, and its symbolic counterpart, the longest common substring. We state and prove a result of Barros, Liao and Rousseau showing that, for rapidly mixing systems, the exponential decay rate of the shortest distance between orbits is given by the correlation dimension of the invariant measure. A central focus of this work is the rigorous verification of the necessary hypotheses for the theorem using the transfer operator. We analyze the spectral properties of
quasi-compact operators on suitable Banach spaces, establishing that the Lasota-Yorke inequality implies the existence of a spectral gap, which in turn guarantees the exponential decay of correlations, with examples and applications.

Orientador: Silvius Klein - PUC-Rio

Banca examinadora:
Lorenzo Justiniano Díaz Casado - PUC-Rio
Manuel Stadlbauer - UFRJ
Jérôme François Alain Jean Rousseau - UFBA
Jiagang Yang - UFF

Desejamos muito sucesso na sua caminhada!!