Evgeny Verbitskiy

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math.DS2025

Gibbs Properties of Equilibrium States

Mirmukhsin Makhmudov, Evgeny Verbitskiy

We consider the problem of equivalence of Gibbs states and equilibrium states for continuous potentials on full shift spaces $E^{Z}$ . Sinai, Bowen, Ruelle and others estab…

math.DS2025

Computation of Lyapunov exponents of matrix products

Aihua Fan, Evgeny Verbitskiy

For $m$ given square matrices $A_{0}, A_{1}, \dots, A_{m - 1}$ ( $m \geq 2$ ), one of which is assumed to be of rank $1$ , and for a given sequence $(ω_{n})$ in $\{0,1, \cdots, m-1\}^\mathbb{N…

math.DS2024

On an extension of a theorem by Ruelle to long-range potentials

Aernout C. D. van Enter, Roberto Fernández, Mirmukhsin Makhmudov +1

Ruelle's transfer operator plays an important role in understanding thermodynamic and probabilistic properties of dynamical systems. In this work, we develop a method of finding ei…