Fixed points of the Ruelle-Thurston operator and the Cauchy transform
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2020
- DOI:
- 10.48550/arXiv.2002.03430
- arXiv:
- arXiv:2002.03430
- Bibcode:
- 2020arXiv200203430L
- Keywords:
-
- Mathematics - Dynamical Systems;
- Mathematics - Complex Variables
- E-Print:
- To appear in Fundamenta Mathematicae