Symmetric and non-symmetric periodic orbits for the digital filter map

Vowden, C.J. and Vowden, B.J. (2008) Symmetric and non-symmetric periodic orbits for the digital filter map. Dynamical Systems - an International Journal, 23 (4). pp. 437-466. ISSN 1468-9367. (The full text of this publication is not available from this repository)

The full text of this publication is not available from this repository. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1080/14689360802169042

Abstract

We exhibit instances of non-symmetric periodic orbits for the digital filter map, resolving a question posed in the literature as to whether such orbits can exist. This piecewise irrational rotation, depending on a parameter a = 2cos , is an isometry of [-1, 1) [-1, 1) and reflections in the two diagonals are time-reversing symmetries for the map. Symmetric orbits are plentiful and have been much investigated. Each periodic orbit is paired with a symbolic string, from the alphabet {-, 0, +}, arising under iteration of the map because of the presence of a line of discontinuity. We prove the existence of an infinite family of non-symmetric orbits where the period N starts at 29 and increases in steps of 5; they correspond to the strings (+00)5(+-)20N-19. We describe several computer algorithms to find non-symmetric periodic orbits and their symbolic strings and list non-symmetric strings both for a = 0.5, and for N 100 across the parameter range. Our evidence suggests that non-symmetric orbits, though not plentiful, are characteristic of the dynamics of the map for all parameter values.

Item Type: Article
Uncontrolled keywords: piecewise rotation; time-reversal symmetry; symbolic dynamics; admissible sequence; non-symmetric orbit
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Louise Dorman
Date Deposited: 31 Mar 2009 11:15
Last Modified: 05 Jun 2009 15:43
Resource URI: http://kar.kent.ac.uk/id/eprint/15303 (The current URI for this page, for reference purposes)
  • Depositors only (login required):