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math.DS2025
The Relative Variational Principle by Ledrappier and Walters: A survey
Anthony Quas
Ledrappier and Walters's article "A Relativised Variational Principle for Continuous Transformations", J. Lond. Math. Soc. (2) 16 (1977), no.3, 568-576) is a landmark in the develo…
math.DS2025
Non-unique equilibrium measures and freezing phase transitions for matrix cocycles for negative
Reza Mohammadpour, Anthony Quas
We consider a one-step matrix cocycle generated by a pair of non-negative parabolic matrices and study the equilibrium measures for as runs over the real…
math.DS2024
BCZ map is weakly mixing
Yitwah Cheung, Anthony Quas
The BCZ map was introduced in 2001 by Boca, Cobeli and Zaharescu as a tool to study the statistical properties of Farey sequences, whose relation to Riemann Hypothesis dates back t…