Dynamics of piecewise smooth functions on the interval

• Grant number: 20/04143-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2020
• End date: May 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Francisco Braun
• Grantee: Richard Rafael Campeiro
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 19/07316-0 - Singularity theory and its applications to differential geometry, differential equations and computer vision, AP.TEM

Abstract

This study aims to develop - as a sequence of the previous scientific iniciation - a deeper study of Discrete Dynamical Systems, more precisely those in which the functions involved are piecewise smooth in an interval I of the real line. It is intended to study the latest work of the researcher B. Pires and collaborators on this subject. It will be used external bibliography in order to gather sufficient knowledge in this area of Mathematics, with the purpose to demonstrate main theorems, lemmas and corollaries involved in these articles. Having obtained the results (demonstrations and examples), the knowledge of Dynamic Systems necessary to understand the recent advances in this area will be unified in a work. (AU)