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Ergodic and qualitative theories of dynamical systems II

Grant number: 19/10269-3
Support type:Research Projects - Thematic Grants
Duration: August 01, 2019 - July 31, 2024
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Claudio Aguinaldo Buzzi
Grantee:Claudio Aguinaldo Buzzi
Home Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
Co-Principal Investigators:Ali Messaoudi ; Paulo Ricardo da Silva
Assoc. researchers:Benito Frazao Pires ; Cláudio Gomes Pessoa ; Douglas Duarte Novaes ; Eduardo Garibaldi ; Marcelo Messias ; Márcio Ricardo Alves Gouveia ; Maurício Firmino Silva Lima ; Patricia Romano Cirilo ; Pedro Toniol Cardin ; Sylvain Philippe Pierre Bonnot ; Tiago de Carvalho ; Vanderlei Minori Horita

Abstract

This project is a continuation of the thematic project: Ergodic and Qualitative Theories of Dynamical Systems (process 2013 / 24541-0). Our goal is to study several problems in the area of dynamical systems and their connections with other areas such as Analysis, Ergodic Theory, Number Theory, Topology among many others. The problems to be addressed are current and include the following topics: Julia sets, infinite matrix dynamics, shadowing, structural stability and ergodicity in linear dynamics, topological dynamics of the composition operator, systems with multiple scales and implicit differential equations, regularization of discontinuous foliations, singular polynomial perturbations, contact partially hyperbolic skew-products, fractal dimensions of non-uniformly expanding repellers, low-discrete KAM solutions for quasi-crystalline interaction models, structural stability, minimality and regularization of non-smooth systems, Thom-Smale program in foliated manifolds, cyclicity and the center-focus problem in three-dimensional manifolds.The main institution is UNESP - S. J. Rio Preto. The team consists of researchers with experience in doctoral supervising and leading research project teams, as well as young researchers. The team has also members from other campuses of UNESP: Ilha Solteira and Presidente Prudente, as well as other institutions of São Paulo State: UNIFESP (São José dos Campos), IME-USP, IMECC-UNICAMP, USP-Ribeirão Preto and UFABC. The project will be guided by the following actions: i) cooperation with high level researches from Brazil and other countries as France, Spain, England, USA, Austria, Chile and Uruguay; ii) participation in conferences and visits to renowned research centers; iii) publication of results in high level scientific journals; iv) training and qualification of human resources in mathematics. (AU)