Bowen-Series transform and thermodynamic formalism for hyperbolic surfaces of finite volume

• Grant number: 11/12338-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: October 01, 2012
• End date: August 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Eduardo Garibaldi
• Grantee: Vincent Pit
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

I plan to continue working on the Bowen-Series coding and use it to study the objects that are related with surfaces with negative curvature. In particular, the exact results of my thesis may allow for precise counting of dynamical quantities like the number of periodic orbits.On another hand, the natural extension of the Bowen-Series transform can be an interesting tool for answering questions about thermodynamic formalism, semi-classical limit and quantification for hyperbolic surfaces.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

GIULIETTI, P.; LOPES, A. O.; PIT, V.. Duality between eigenfunctions and eigendistributions of Ruelle and Koopman operators via an integral kernel. Stochastics and Dynamics, v. 16, n. 3, SI, JUN 2016. (11/12338-0)

PIT, VINCENT; SCHAPIRA, BARBARA. FINITENESS OF GIBBS MEASURES ON NONCOMPACT MANIFOLDS WITH PINCHED NEGATIVE CURVATURE. ANNALES DE L INSTITUT FOURIER, v. 68, n. 2, p. 457-510, 2018. (11/12338-0)

GIULIETTI, P.; LOPES, A. O.; PIT, V.. Duality between eigenfunctions and eigendistributions of Ruelle and Koopman operators via an integral kernel. Stochastics and Dynamics, v. 16, n. 3, p. 22-pg., 2016-06-01. (11/12338-0)