Universal functions for the Sharkovsky classes of maps

2021/06/20 by V. Kannan, Kannan, V., Pabitra Narayan Mandal +1
Mathematics · Physics and Astronomy · #26A18 #37C25 #37E15 #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2106.10647

openalex publication_date 2021/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We exhibit a single interval map (called universal map) that admits all those orbit patterns which are available in the first Sharkovsky class. An interval map is said to be in the first Sharkovsky class if every periodic point of it is a fixed point. This provides a way to find universal maps in the class of contractions on interval. We also characterize all such universal maps in the first Sharkovsky class.

Related

• Sharkovsky's Ordering in the Mandelbrot Set
• Interval maps where every point is eventually fixed
• Sharkovsky's Theorem and one-dimensional combinatorial dynamics
• From the Sharkovskii theorem to periodic orbits for the Rössler system
• A collection of simple proofs of Sharkovsky's theorem