Beyond transitivity for linear operators on infinite dimension

• Grant number: 21/08199-7
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: October 31, 2021
• End date: April 29, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Patricia Romano Cirilo
• Grantee: Felipe Hikari Kawahama
• Supervisor: Enrique Ramiro Pujals
• Host Institution: Instituto de Ciência e Tecnologia (ICT). Universidade Federal de São Paulo (UNIFESP). Campus São José dos Campos. São José dos Campos , SP, Brazil
• Institution abroad: City University of New York (CUNY), United States
• Associated to the scholarship: 19/20500-4 - Abundance of transitive linear operators in infinite dimension, BP.MS

Abstract

The aim of the research project to be developed during the internship abroad is divided in two parts: (i) to explore if it is possible to characterize those infinite dimensional operator such that their non-wandering set is robustly transitive (ii) For any operator or at least for generic ones, to explore the possibility of finding a spectral decomposition of the non-wandering set (or the chain recurrent) in closed invariant transitive subspaces.