Scalings in circle maps II

Authors

F. M. Tangerman, Stony Brook University
J. J. P. Veerman, Portland State UniversityFollow

Published In

Communications in Mathematical Physics

Document Type

Citation

Publication Date

10-1991

Abstract

In this paper we consider one parameter families of circle maps with nonlinear flat spot singularities. Such circle maps were studied in [Circles I] where in particular we studied the geometry of closest returns to the critical interval for irrational rotation numbers of constant type. In this paper we apply those results to obtain exact relations between scalings in the parameter space to dynamical scalings near parameter values where the rotation number is the golden mean. Then results on [Circles I] can be used to compute the scalings in the parameter space. As far as we are aware, this constitutes the first case in which parameter scalings can be rigorously computed in the presence of highly nonlinear (and nonhyperbolic) dynamics.

Rights

Copyright (1991) Springer

Locate the Document

https://doi-org/10.1007/BF02101506

DOI

10.1007/BF02101506

Persistent Identifier

https://archives.pdx.edu/ds/psu/36123

Citation Details

Tangerman, F.M., Veerman, J.J.P. Scalings in circle maps II. Commun.Math. Phys. 141, 279–291 (1991). https://doi-org/10.1007/BF02101506