LAUSR.org creates dashboard-style pages of related content for over 1.5 million academic articles. Sign Up to like articles & get recommendations!

Quasi-graphs, zero entropy and measures with discrete spectrum

Photo from wikipedia

In this paper, we study dynamics of maps on quasi-graphs and characterise their invariant measures. In particular, we prove that every invariant measure of a quasi-graph map with zero topological… Click to show full abstract

In this paper, we study dynamics of maps on quasi-graphs and characterise their invariant measures. In particular, we prove that every invariant measure of a quasi-graph map with zero topological entropy has discrete spectrum. Additionally, we obtain an analog of Llibre–Misiurewicz’s result relating positive topological entropy with existence of topological horseshoes. We also study dynamics on dendrites and show that if a continuous map on a dendrite whose set of all endpoints is closed and has only finitely many accumulation points, has zero topological entropy, then every invariant measure supported on an orbit closure has discrete spectrum.

Keywords: discrete spectrum; entropy; quasi graphs; topological entropy

Journal Title: Nonlinearity
Year Published: 2022

Link to full text (if available)


Share on Social Media:                               Sign Up to like & get
recommendations!

Related content

More Information              News              Social Media              Video              Recommended



                Click one of the above tabs to view related content.