Correlation Number for Potentials with Entropy Gaps and Cusped Hitchin Representations

2024/12/30 by Kao, Lien-Yung, Martone, Giuseppe · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2412.20627

Abstract

We introduce a correlation number for two strictly positive, locally Hölder continuous, independent potentials with strong entropy gaps at infinity on a topologically mixing countable state Markov shift with BIP. We define in this way a correlation number for pairs of cusped Hitchin representations. Furthermore, we explore the connection between the correlation number and the Manhattan curve, along with several rigidity properties of this correlation number.

Cited by

• Gurevic pressure and equidistribution for amenable extensions of countable state Markov shifts
• Manhattan curves in complex dynamics and asymptotic correlation of multiplier spectra

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