Robustly Transitive Endomorphisms and Strong Volume Expansion for Toral Endomorphisms

Robustly Transitive Endomorphisms and Strong Volume Expansion for Toral Endomorphisms

Explore a 49-minute lecture on robust transitivity for partially hyperbolic endomorphisms of the two torus, presented by Martin Andersson from Universidade Federal Fluminense as part of the Simons Semester on Dynamics. Delve into a new criterion for robust transitivity, focusing on endomorphisms whose action in the first homology has two integer eigenvalues greater than one. Learn about the condition where the Jacobian being everywhere greater than the largest eigenvalue leads to robust transitivity. Discover how Blichfedt's theorem is introduced as a tool for extracting dynamical information from the map's action in homology. Gain insights into this advanced topic in dynamical systems and its implications for toral endomorphisms.