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arXiv · 2404.03780

Authomorphic measures with negative exponents for multicritical circle maps

Nataliya Goncharuk·Michael Yampolsky
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Abstract

Authomorphic or $s$-measures for circle diffeomorphisms were introduced by R.Douady and J.-C. Yoccoz in 1999. They have multiple applications in circle dynamics, with the case $s=-1$ being particularly important for describing conjugacy classes. In arxiv:2306.13524, 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.

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Nataliya Goncharuk, Michael Yampolsky. 2024-04-04. Authomorphic measures with negative exponents for multicritical circle maps. https://doi.org/10.3934/dcds.2024169

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