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We give necessary and sufficient conditions for a function in a naturally appearing functional space to be a fixed point of the Ruelle-Thurston operator associated to a rational function, see Lemma 2.1. The proof uses essentially a recent [13]. As an immediate consequence, we revisit Theorem 1 and Lemma 5.2 of [11], see Theorem 1 and Lemma 2.2 below.
Let $Gamma$ be a co-compact Fuchsian group of isometries on the Poincare disk $DD$ and $Delta$ the corresponding hyperbolic Laplace operator. Any smooth eigenfunction $f$ of $Delta$, equivariant by $Gamma$ with real eigenvalue $lambda=-s(1-s)$, where
In 1980s, Thurston established a combinatorial characterization for post-critically finite rational maps. This criterion was then extended by Cui, Jiang, and Sullivan to sub-hyperbolic rational maps. The goal of this paper is to present a new but sim
We consider a generalization of the Ruelle theorem for the case of continuous time problems. We present a result which we believe is important for future use in problems in Mathematical Physics related to $C^*$-Algebras We consider a finite state set
Given an iterated function system of affine dilations with fixed points the vertices of a regular polygon, we characterize which points in the limit set lie on the boundary of its convex hull.
At each time $ninmathbb{N}$, let $bar{Y}^{(n)}=(y_{1}^{(n)},y_{2}^{(n)},cdots)$ be a random sequence of non-negative numbers that are ultimately zero in a random environment $xi=(xi_{n})_{ninmathbb{N}}$ in time, which satisfies for each $ninmathbb{N}