Scalings in Circle Maps (I)

Authors

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

Published In

Communications in Mathematical Physics

Document Type

Citation

Publication Date

11-1990

Abstract

Letf be a “flat spot” circle map with irrational rotation number. Located at the edges of the flat spot are non-flat critical points (S: x→Ax v,v≧1). First, we define scalings associated with the closest returns of the orbit of the critical point. Under the assumption that these scalings go to zero, we prove that the derivative of long iterates of the critical value can be expressed in the scalings. The asymptotic behavior of the derivatives and the scalings can then be calculated. We concentrate on the cases for which one can prove the above assumption. In particular, let one of the singularities be linear. These maps arise for example as the lower bound of the non-decreasing truncations of non-invertible bimodal circle maps. It follows that the derivatives grow at a sub-exponential rate.

Rights

Copyright (1990) Springer

Locate the Document

https://doi-org/10.1007/BF02102091

DOI

10.1007/BF02102091

Persistent Identifier

https://archives.pdx.edu/ds/psu/36111

Citation Details

Veerman, J. J. P., & Tangerman, F. M. (1990). Scalings in circle maps (I). Communications in mathematical physics, 134(1), 89-107.