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.
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| 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) |
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