Work

Authomorphic measures with negative exponents for multicritical circle maps

Year: 2024

Type: article

Abstract: Authomorphic or $ s $-measures for circle diffeomorphisms were introduced by R. Douady and J.-C. Yoccoz [1]. They have multiple applications in circle dynamics, with the case $ s = -1 $ being particularly important for describing conjugacy classes. In [5], E. de Faria, P. Guarino and B. Nussenzveig proved existence and uniqueness of automorphic $ s $-measures for multicritical circle maps for all $ s>0 $. The purpose of this paper is to extend these results to $ s $-measures with negative values of $ s $. As an application, we prove a smoothness result for irrational Arnold tongues in families of multicritical maps.

Source: Discrete and Continuous Dynamical Systems

DOI: 10.3934/dcds.2024169

Authors: Nataliya Goncharuk, Michael Yampolsky

Institution: Texas A&M University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4405205100

FWCI:

Cites: 7

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Related to: 10