Full text
| |
| Author(s): |
Bella Rocxane Martins Figliaggi
Total Authors: 1
|
| Document type: | Master's Dissertation |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2025-07-23 |
| Examining board members: |
Tiago Pereira da Silva;
Daniel Smania Brandão;
Anna Maria Cherubini;
Katrin Grit Gelfert
|
| Advisor: | Tiago Pereira da Silva |
| Abstract | |
This masters thesis studies the statistical behavior of dynamical systems through the evolution of densities. Focusing on invariant and stationary measures, respectively, for deterministic and random dynamical systems, we explore how such measures capture the long-term dynamics. Using the framework of Markov and transfer operators, we presented a review on well-known conditions for the existence and stability of these measures, analyzed their ergodic and mixing properties, and provided new proofs for results involving systems with additive noise and non-uniform expansion. The final chapter applies these ideas to iterated function systems. (AU) | |
| FAPESP's process: | 23/06566-8 - Stationary Measures for Random Dynamical Systems |
| Grantee: | Bella Rocxane Martins Figliaggi |
| Support Opportunities: | Scholarships in Brazil - Master |