Uniformization of tongues in double standard map family and variation of maximal chaotic sets *
Abstract
Abstract We study hyperbolic components, also known as tongues , in the double standard map family comprising circle maps of the form: f a , b ( x ) = ( 2 x + a + b π sin ( 2 π x ) ) mod 1 , a ∈ R / Z , 0 ⩽ b ⩽ 1. We prove simple connectedness of tongues by providing a dynamically natural real-analytic uniformization for each tongue. For maps in a tongue, we characterize the unique maximal subset of the circle on which f a , b is Devaney chaotic. We also show that the Hausdorff dimension of this maximal chaotic set varies real-analytically inside a tongue.
Fields of Study & Subjects
Linguistics and Cultural Studies
Publication details
- Journal / source
- Nonlinearity
- Volume
- 39
- Issue
- 7
- Pages
- 075025–075025
- Publication date
- 24 July 2026
- Language
- EN