Computation of symbolic dynamics for one-dimensional maps

DOI10.1016/j.cam.2009.12.034zbMath1195.65216OpenAlexW1981928883MaRDI QIDQ964963

Lorenzo Sella, Peter J. Collins

Publication date: 21 April 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2009.12.034

zbMATH Keywords

algorithmscritical pointsinterval arithmeticsymbolic dynamicsentropy boundsone-dimensional mapsingular limitdiscontinuitykneading theoryVan der Pol equationswitching systempiecewise-monotone-continuous maps

Mathematics Subject Classification ID

General methods in interval analysis (65G40) Dynamical systems involving maps of the interval (37E05) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25) Numerical problems in dynamical systems (65P99)

Uses Software

• PNM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An improved algorithm for computing topological entropy
• Computing the topological entropy of maps
• What you need to know to knead
• Fredholm determinant for piecewise linear transformations
• Chaos generation using binary hysteresis
• Volume growth and entropy
• Computing the topological entropy of maps of the interval with three monotone pieces
• Symbolic dynamics. One-sided, two-sided and countable state Markov shifts
• Entropy invariants. I: The universal order relation of order-preserving star products.
• Entropy invariants. II: The block structure of Stefan matrices.
• Weighted kneading theory of one-dimensional maps with a hole
• Kneading theory: a functorial approach
• Kneading theory for tree maps
• Entropy of piecewise monotone mappings
• An Example Where Topological Entropy is Continuous
• An extension of the theorem of Milnor and Thurston on the zeta functions of interval maps
• BORDER-COLLISION BIFURCATIONS FOR PIECEWISE SMOOTH ONE-DIMENSIONAL MAPS
• TRIMODAL MAPS
• On Iterated Maps of the Interval with Holes
• The Forced van der Pol Equation I: The Slow Flow and Its Bifurcations
• An Introduction to Symbolic Dynamics and Coding

This page was built for publication: Computation of symbolic dynamics for one-dimensional maps