2008/02/18 by Kuo-Chang Chen, Chen, Kuo-Chang, Xun Dong +1
Mathematics · Physics and Astronomy · #37E05 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:37E05
paper · pdf · doi:10.48550/arxiv.0802.2445
15 pages
arxiv created 2008/02/18 · openalex publication_date 2008/02/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well known that the time average or the center of mass for generic orbits of the standard tent map is 0.5. In this paper we show some interesting properties of the exceptional orbits, including periodic orbits, orbits without mass center, and orbits with mass centers different from 0.5. We prove that for any positive integer n, there exist n distinct periodic orbits for the standard tent map with the same center of mass, and the set of mass centers of periodic orbits is a dense subset of [0,2/3]. Considering all possible orbits, then the set of mass centers is the interval [0,2/3]. Moreover, for every x in [0,2/3], there are uncountably many orbits with mass center x. We also show that there are uncountably many orbits without mass center.