Hamiltonian dynamics near critical energy levels and homoclinic orbits to the central manifold of a saddle-center

• Grant number: 09/18586-6
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: April 01, 2010
• End date: March 31, 2014
• 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

Abstract

In this project, the student Naiara will study Hamiltonian systems with two degrees of freedom in energy levels near critical levels containing saddle-center equillibrium points. The aim is to give sufficient conditions for the existence of transverse sections of the flow in such energy levels and, as a consequence, obtain homoclinic orbits to the central manifold of the saddle-center.

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.. 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)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

PAULO, Naiara Vergian de. Systems of transverse sections near critical levels of Hamiltonian systems in $\\mathbb R ^4$. 2014. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME/SBI) São Paulo.