Applied symbolic dynamics: attractors and filtrations

Previous Article
Anti-periodic solutions to a class of non-monotone evolution equations
DCDS Home
This Issue
Next Article
Stability of symmetric periodic solutions with small amplitude of $\dot x(t)=\alpha f(x(t), x(t-1))$

January 1999, 5(1): 43-60. doi: 10.3934/dcds.1999.5.43

Applied symbolic dynamics: attractors and filtrations

George Osipenko ^1, and Stephen Campbell ^2,

1.	Laboratory of Nonlinear Analysis and Mathematical Modelling, St.-Petersburg State Technical University, 195251, Russian Federation
2.	Department of Mathematics, Belmont University, Nashville, TN, United States

Received May 1995 Revised January 1997 Published October 1998

Abstract
Related Papers

This paper is a study of the global structure of the attractors of a dynamical system. The dynamical system is associated with an oriented graph called a Symbolic Image of the system. The symbolic image can be considered as a finite discrete approximation of the dynamical system flow. Investigation of the symbolic image provides an opportunity to localize the attractors of the system and to estimate their domains of attraction. A special sequence of symbolic images is considered in order to obtain precise knowledge about the global structure of the attractors and to get filtrations of the system.

Keywords: homeomorphism., symbolic dynamics, Attractors, discrete dynamical system.

Mathematics Subject Classification: 37B1.

Citation: George Osipenko, Stephen Campbell. Applied symbolic dynamics: attractors and filtrations. Discrete & Continuous Dynamical Systems - A, 1999, 5 (1) : 43-60. doi: 10.3934/dcds.1999.5.43

[1]	Steven T. Piantadosi. Symbolic dynamics on free groups. Discrete & Continuous Dynamical Systems - A, 2008, 20 (3) : 725-738. doi: 10.3934/dcds.2008.20.725
[2]	Howard A. Levine, Yeon-Jung Seo, Marit Nilsen-Hamilton. A discrete dynamical system arising in molecular biology. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 2091-2151. doi: 10.3934/dcdsb.2012.17.2091
[3]	Safya Belghith. Symbolic dynamics in nondifferentiable system originating in R-L-Diode driven circuit. Discrete & Continuous Dynamical Systems - A, 2000, 6 (2) : 275-292. doi: 10.3934/dcds.2000.6.275
[4]	Jim Wiseman. Symbolic dynamics from signed matrices. Discrete & Continuous Dynamical Systems - A, 2004, 11 (2&3) : 621-638. doi: 10.3934/dcds.2004.11.621
[5]	Michael Hochman. A note on universality in multidimensional symbolic dynamics. Discrete & Continuous Dynamical Systems - S, 2009, 2 (2) : 301-314. doi: 10.3934/dcdss.2009.2.301
[6]	Mohammadreza Molaei. Hyperbolic dynamics of discrete dynamical systems on pseudo-riemannian manifolds. Electronic Research Announcements, 2018, 25: 8-15. doi: 10.3934/era.2018.25.002
[7]	Jose S. Cánovas, Tönu Puu, Manuel Ruiz Marín. Detecting chaos in a duopoly model via symbolic dynamics. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 269-278. doi: 10.3934/dcdsb.2010.13.269
[8]	Nicola Soave, Susanna Terracini. Symbolic dynamics for the $N$-centre problem at negative energies. Discrete & Continuous Dynamical Systems - A, 2012, 32 (9) : 3245-3301. doi: 10.3934/dcds.2012.32.3245
[9]	Dieter Mayer, Fredrik Strömberg. Symbolic dynamics for the geodesic flow on Hecke surfaces. Journal of Modern Dynamics, 2008, 2 (4) : 581-627. doi: 10.3934/jmd.2008.2.581
[10]	Frédéric Naud. Birkhoff cones, symbolic dynamics and spectrum of transfer operators. Discrete & Continuous Dynamical Systems - A, 2004, 11 (2&3) : 581-598. doi: 10.3934/dcds.2004.11.581
[11]	Fryderyk Falniowski, Marcin Kulczycki, Dominik Kwietniak, Jian Li. Two results on entropy, chaos and independence in symbolic dynamics. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3487-3505. doi: 10.3934/dcdsb.2015.20.3487
[12]	David Ralston. Heaviness in symbolic dynamics: Substitution and Sturmian systems. Discrete & Continuous Dynamical Systems - S, 2009, 2 (2) : 287-300. doi: 10.3934/dcdss.2009.2.287
[13]	Hunseok Kang. Dynamics of local map of a discrete Brusselator model: eventually trapping regions and strange attractors. Discrete & Continuous Dynamical Systems - A, 2008, 20 (4) : 939-959. doi: 10.3934/dcds.2008.20.939
[14]	Wen-Guei Hu, Song-Sun Lin. On spatial entropy of multi-dimensional symbolic dynamical systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (7) : 3705-3717. doi: 10.3934/dcds.2016.36.3705
[15]	H. M. Hastings, S. Silberger, M. T. Weiss, Y. Wu. A twisted tensor product on symbolic dynamical systems and the Ashley's problem. Discrete & Continuous Dynamical Systems - A, 2003, 9 (3) : 549-558. doi: 10.3934/dcds.2003.9.549
[16]	Mădălina Roxana Buneci. Morphisms of discrete dynamical systems. Discrete & Continuous Dynamical Systems - A, 2011, 29 (1) : 91-107. doi: 10.3934/dcds.2011.29.91
[17]	Yejuan Wang, Chengkui Zhong, Shengfan Zhou. Pullback attractors of nonautonomous dynamical systems. Discrete & Continuous Dynamical Systems - A, 2006, 16 (3) : 587-614. doi: 10.3934/dcds.2006.16.587
[18]	Bernd Aulbach, Martin Rasmussen, Stefan Siegmund. Approximation of attractors of nonautonomous dynamical systems. Discrete & Continuous Dynamical Systems - B, 2005, 5 (2) : 215-238. doi: 10.3934/dcdsb.2005.5.215
[19]	Alfredo Marzocchi, Sara Zandonella Necca. Attractors for dynamical systems in topological spaces. Discrete & Continuous Dynamical Systems - A, 2002, 8 (3) : 585-597. doi: 10.3934/dcds.2002.8.585
[20]	Anke D. Pohl. Symbolic dynamics for the geodesic flow on two-dimensional hyperbolic good orbifolds. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 2173-2241. doi: 10.3934/dcds.2014.34.2173

2017 Impact Factor: 1.179

American Institute of Mathematical Sciences