Skip to Main content Skip to Navigation
Conference papers

Pattern avoidance in dynamical systems

Abstract : Orbits generated by discrete-time dynamical systems have some interesting combinatorial properties. In this paper we address the existence of forbidden order patterns when the dynamics is generated by piecewise monotone maps on one-dimensional closed intervals. This means that the points belonging to a sufficiently long orbit cannot appear in any arbitrary order. The admissible patterns are then (the inverses of) those permutations avoiding the so-called forbidden root patterns in consecutive positions. The last part of the paper studies and enumerates forbidden order patterns in shift systems, which are universal models in information theory, dynamical systems and stochastic processes. In spite of their simple structure, shift systems exhibit all important features of low-dimensional chaos, allowing to export the results to other dynamical systems via order-isomorphisms. This paper summarizes some results from [1] and [11].
Complete list of metadata

Cited literature [13 references]  Display  Hide  Download

https://hal.inria.fr/hal-01185170
Contributor : Coordination Episciences Iam <>
Submitted on : Wednesday, August 19, 2015 - 11:43:37 AM
Last modification on : Wednesday, June 26, 2019 - 4:36:03 PM
Long-term archiving on: : Friday, November 20, 2015 - 10:40:44 AM

File

dmAJ0107.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01185170, version 1

Collections

Citation

José María Amigó, Sergi Elizalde, Matthew B. Kennel. Pattern avoidance in dynamical systems. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.71-82. ⟨hal-01185170⟩

Share

Metrics

Record views

76

Files downloads

867