2013/02/13 by Roman Hric, Tobias Jäger, Hric, Roman +1
Mathematics · Physics and Astronomy · #37A05 #37E30 #37E30. Primary 54H20 #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary 54H20 #Quantum chaos and dynamical systems #math.DS #msc:37A05 #msc:37E30 #msc:37E30. #msc:54H20
paper · pdf · doi:10.48550/arxiv.1302.3024
16 pages, 4 figures
arxiv created 2013/02/13 · openalex publication_date 2013/02/13 · arxiv updated 2013/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe a general procedure to construct topological extensions of given skew product maps with one-dimensional fibres, by blowing up a countable number of single points to vertical segments. This allows to produce various examples of unusual dynamics, including almost automorphic minimal sets of almost periodically forced systems, point-distal but non-distal homeomorpisms of the torus (as first constructed by Rees) or minimal sets of quasiperiodically forced interval maps which are not filled-in.