Multidimensional piecewise contractions and applications

• Grant number: 25/14256-4
• Support Opportunities: Regular Research Grants
• Start date: November 01, 2025
• End date: October 31, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Benito Frazao Pires
• Grantee: Benito Frazao Pires
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil
• City of the host institution: Ribeirão Preto

Abstract

Piecewise contractions are piecewise smooth maps from Rn that contract the distance between pairs of points within the same domain of continuity. The dynamics of such maps is rich, consisting of periodic attractors and fractal attractors. Recently, some progress has been made by the author, his collaborators and other researchers in understanding the dynamics of such maps in the multidimensional case. This project will continue the study of multidimensional piecewise contractions, including possible applications to the dynamics of multidimensional contracted rotations, switched server systems and Hopfied neural networks. (AU)