Systems of transverse sections in classical mechanics

• Grant number: 14/08113-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2014
• End date: April 17, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Pedro Antonio Santoro Salomão
• Grantee: Naiara Vergian de Paulo
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 11/16265-8 - Low dimensional dynamics, AP.TEM

Abstract

In this project, we study the existence of systems of transverse sections for Hamiltonian flows with two degrees of freedom, restricted to contact-type energy levels. We use the theory of pseudo-holomorphic curves in symplectizations to prove the existence of such transverse sections in energy levels close to critical levels containing saddle-center equilibrium points. We intend to apply these results to classical Hamiltonian systems such as the restricted three body problem.

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)

DE PAULO, NAIARA V.; SALOMAO, PEDRO A. S.. ON THE MULTIPLICITY OF PERIODIC ORBITS AND HOMOCLINICS NEAR CRITICAL ENERGY LEVELS OF HAMILTONIAN SYSTEMS IN R-4. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 372, n. 2, p. 859-887, JUL 15 2019. (16/25053-8, 14/08113-1)

DE PAULO, NAIARA V.; SALOMAO, PEDRO A. S.. Systems of Transversal Sections Near Critical Energy Levels of Hamiltonian Systems in R-4. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 252, n. 1202, p. 1+, MAR 2018. (09/18586-6, 14/08113-1, 11/16265-8, 13/20065-0)