Work

On Zero Entropy Homeomorphisms of the Pseudo-arc

Year: 2024

Type: article

Abstract: In this paper we study interval maps f with zero topological entropy that are crooked; i.e. whose inverse limit with f as the single bonding map is the pseudo-arc. We show that there are uncountably many zero entropy pairwise non-conjugate zero entropy crooked interval maps with different sets of fixed points. We also show that there are uncountably many crooked maps that are pairwise non-conjugate and have exactly two fixed points. Furthermore, we provide a characterization of crooked interval maps that are under or above the diagonal.

Source: Qualitative Theory of Dynamical Systems

DOI: 10.1007/s12346-024-01126-5

Author: Jernej Činč

Institutions: The Abdus Salam International Centre for Theoretical Physics (ICTP), University of Maribor

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: European Commission, Javna Agencija za Raziskovalno Dejavnost RS, HORIZON EUROPE Framework Programme