Finite-Expansivity and N-Shadowing

• Autores: Carrasco-Olivera D., Lee K., Morales C.A., Villavicencio H.
• Formato: artículo
• Fecha de Publicación: 2021
• Institución: Consejo Nacional de Ciencia Tecnología e Innovación
• Repositorio: CONCYTEC-Institucional
• Lenguaje: inglés
• OAI Identifier: oai:repositorio.concytec.gob.pe:20.500.12390/2427
• Enlace del recurso: https://hdl.handle.net/20.500.12390/2427; https://doi.org/10.1007/s00574-021-00253-w
• Nivel de acceso: acceso abierto
• Materia: N-shadowing; Homeomorphism; http://purl.org/pe-repo/ocde/ford#1.01.01

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. © 2021, Sociedade Brasileira de Matemática.