Decay of correlations and statistical properties for geodesic flows in nonpositive curvature

• Grant number: 24/22093-5
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: August 01, 2025
• End date: March 31, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Yuri Gomes Lima
• Grantee: Yuri Gomes Lima
• Visiting researcher: Ian Steven Melbourne
• Visiting researcher institution: University Of Warwick/Uw, England
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The project aims at developing the powerful tools of dynamical billiards in the context of geodesic flows in nonpositive curvature, showing that these latter do possess a varied possibility of statistical behavior of decay of correlations, (standard and non-standart) central limit theorem and functional central limit theorem. (AU)