Symbolic Dynamics of Order-Preserving Orbits

Authors

J. J. P. Veerman, Portland State UniversityFollow

Published In

Physica D: Nonlinear Phenomena

Document Type

Citation

Publication Date

11-1987

Abstract

The maps we consider are roughly those that can be obtained by truncating non-invertible maps to weakly monotonic maps (they have a flat piece). The binary sequences that correspond to order-preserving orbits are shown to satisfy a minimax principle (which was already known for order-preserving orbits with rational rotation number). The converse is also proven: all minimax orbits are order-preserving with respect to some rotation number.

For certain families of such circle maps one can solve exactly for the parameter values for which the map has a specified rotation number rho. For rho rational we obtain the endpoints of the resonance intervals recursively. These parameter values can be organized in a natural way as the nodes of a Farey tree. We give some applications of the ideas discussed.

Rights

Copyright © 1987 Published by Elsevier B.V.

Description

*At the time of publication, Peter Veerman was affiliated with Cornell University.

Locate the Document

https://doi.org/10.1016/0167-2789(87)90055-8

DOI

10.1016/0167-2789(87)90055-8

Persistent Identifier

https://archives.pdx.edu/ds/psu/36016

Citation Details

Veerman, P. (1987). Symbolic dynamics of order-preserving orbits. Physica D: Nonlinear Phenomena, 29(1-2), 191-201.