Simple dynamical systems
In this paper, we study the class of simple systems on R induced by homeomorphisms having finitely many non-ordinary points. We characterize the family of homeomorphisms on R having finitely many non-ordinary points upto (order) conjugacy. For x,y ∈ R, we say x ∼ y on a dynamical system (R,f) if x and y have same dynamical properties, which is an equivalence relation. Said precisely, x ∼ y if there exists an increasing homeomorphism h : R → R such that h ◦ f = f ◦ h and h(x) = y. An element x ∈ R is ordinary in (R,f) if its equivalence class [x] is a neighbourhood of it.
L. S. Block and W. A. Coppel, Dynamics in One Dimension, Volume 1513 of Lecture Notes in Mathematics, Springer-Verlag, Berline, 1992. https://doi.org/10.1007/BFb0084762
L. Block and E. Coven, Topological conjugacy and transitivity for a class of piecewise monotone maps of the interval, Trans. Amer. Math. Soc. 300 (1987), 297-306. https://doi.org/10.1090/S0002-9947-1987-0871677-X
M. Brin and G. Stuck, Introduction to Dynamical Systems, Cambridge University Press, 2002. https://doi.org/10.1017/CBO9780511755316
R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley Publishing Company Advanced Book Program, Redwood City, CA, second edition, 1989.
R. A. Holmgren, A First Course in Discrete Dynamical Systems, Springer-Verlag, New York, 1996. https://doi.org/10.1007/978-1-4419-8732-7
S. Sai, Symbolic dynamics for complete classification, Ph.D Thesis, University of Hyderabad, 2000.
B. Sankara Rao, I. Subramania Pillai and V. Kannan, The set of dynamically special points, Aequationes Mathematicae 82, no. 1-2 (2011), 81-90. https://doi.org/10.1007/s00010-010-0066-6
A. N. Sharkovskii, Coexistence of cycles of a continuous map of a line into itself, Ukr. Math. Z. 16 (1964), 61-71.
Metrics powered by PLOS ALM
Cited-By (articles included in Crossref)
This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site
1. Which orbit types force only finitely many orbit types?
V. Kannan, Pabitra Narayan Mandal
Journal of Difference Equations and Applications vol: 26 issue: 5 first page: 676 year: 2020
Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
Universitat Politècnica de València
e-ISSN: 1989-4147 https://doi.org/10.4995/agt