Computation of symbolic dynamics for one-dimensional maps

被引：5
作者：
Sella, Lorenzo [1 ]
Collins, Pieter [1 ]
机构：
[1] Ctr Wiskunde & Informat, NL-1090 GB Amsterdam, Netherlands
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2010年 / 234卷 / 02期
关键词：
One-dimensional map; Kneading theory; Symbolic dynamics; Interval arithmetic; TOPOLOGICAL-ENTROPY; KNEADING THEORY; INVARIANTS; INTERVAL;
D O I：
10.1016/j.cam.2009.12.034
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we design and implement rigorous algorithms for computing symbolic dynamics for piecewise-monotone-continuous maps of the interval. The algorithms are based on computing forwards and backwards approximations of the boundary, discontinuity and critical points. We explain how to handle the discontinuities in the symbolic dynamics which occur when the computed partition element boundaries are not disjoint. The method is applied to compute the symbolic dynamics and entropy bounds for the return map of the singular limit of a switching system with hysteresis and the forced Van der Pol equation. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码：418 / 436
页数：19
相关论文
共 50 条
  • [41] Dual star products and symbolic dynamics of Lorenz maps with the same entropy
    Peng, SL
    Du, LM
    [J]. PHYSICS LETTERS A, 1999, 261 (1-2) : 63 - 73
  • [42] From One-dimensional to Two-dimensional Cellular Automata
    Dennunzio, Alberto
    [J]. FUNDAMENTA INFORMATICAE, 2012, 115 (01) : 87 - 105
  • [43] CHAOS ON ONE-DIMENSIONAL COMPACT METRIC SPACES
    Kocan, Zdenek
    [J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2012, 22 (10):
  • [44] Chaotic properties of a one-dimensional Lorentz gas
    Appert, C
    Bokel, C
    Dorfman, JR
    Ernst, MH
    [J]. PHYSICA D-NONLINEAR PHENOMENA, 1997, 103 (1-4) : 357 - 361
  • [45] Generalized horseshoes and indecomposability for one-dimensional continua
    Ye X.
    [J]. Ukrainian Mathematical Journal, 1998, 50 (8) : 1192 - 1200
  • [46] Combinatorics of one-dimensional simple Toeplitz subshifts
    Sell, Daniel
    [J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2020, 40 (06) : 1673 - 1714
  • [47] Hyperbolicity as an obstruction to smoothability for one-dimensional actions
    Bonatti, Christian
    Lodha, Yash
    Triestino, Michele
    [J]. GEOMETRY & TOPOLOGY, 2019, 23 (04) : 1841 - 1876
  • [48] Decimation and interleaving operations in one-sided symbolic dynamics
    Abram, William C.
    Lagarias, Jeffrey C.
    Slonim, Daniel J.
    [J]. ADVANCES IN APPLIED MATHEMATICS, 2021, 126
  • [49] Complex Symbolic Dynamics of One Class of Cellular Automata Rules
    Tang, Changbing
    Chen, Fangyue
    Jin, Weifeng
    [J]. 2009 INTERNATIONAL WORKSHOP ON CHAOS-FRACTALS THEORIES AND APPLICATIONS (IWCFTA 2009), 2009, : 236 - +
  • [50] Symbolic computation with finite biquandles
    Creel, Conrad
    Nelson, Sam
    [J]. JOURNAL OF SYMBOLIC COMPUTATION, 2007, 42 (10) : 992 - 1000
12345