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arXiv · 2305.16022

Counting periodic orbits on fractals weighted by their Lyapunov exponents

Ugo Bessi
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Abstract

Several authors have shown that Kusuoka's measure $\kappa$ on fractals is a scalar Gibbs measure; in particular, it maximises a pressure. There is also a different approach, in which one defines a matrix-valued Gibbs measure $\mu$ which induces both Kusuoka's measure $\kappa$ and Kusuoka's bilinear form. In the first part of the paper we show that one can define a "pressure" for matrix valued measures; this pressure is maximised by $\mu$. In the second part, we use the matrix-valued Gibbs measure $\mu$ to count periodic orbits on fractals, weighted by their Lyapounov exponents.

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Ugo Bessi. 2023-05-25. Counting periodic orbits on fractals weighted by their Lyapunov exponents. https://arxiv.org/abs/2305.16022

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