Finite-Expansivity and N-Shadowing

Carrasco-Olivera D.; Lee K.; Morales C.A.; Villavicencio H. · Bulletin of the Brazilian Mathematical Society (2022) · DOI: 10.1007/s00574-021-00253-w

Resumen

We prove that every finite-expansive homeomorphism with the shadowing property has a kind of stability. This stability will be good enough to imply both the shadowing property and the denseness of periodic points in the chain recurrent set. Next we analyze the N-shadowing property which is really stronger than the multishadowing property in Cherkashin and Kryzhevich (Topol Methods Nonlinear Anal 50(1): 125–150, 2017). We show that an equicontinuous homeomorphism has the N-shadowing property for some positive integer N if and only if it has the shadowing property.

Instituciones: Universidad Nacional de Ingeniería