Symplectic classification of parameterized curve-germs and Lagrangian stars

Author(s)

Fausto Assunção de Brito Lira

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2015-03-27

Examining board members

Roberta Godoi Wik Atique; João Carlos Ferreira Costa; Marcos Craizer; Abramo Hefez; Marcelo José Saia

• Advisor: Roberta Godoi Wik Atique; Wojciech Domitrz

Abstract

This work aims the symplectic classification of parametrized curve-germs and Lagrangian stars using the method of algebraic restrictions. We classify simplecticaly parametrized curve-germs with semigroups (4; 5; 6); (4; 5; 7) e (4; 5; 6; 7) We introduce an invariant for algebraic restrictions to quasi-homogeneous parametrized curve-germs: the proportional minimum quasi degree part. By the method of algebraic restrictions, this invariant is able to distinguish different orbits of parameterized quasi-homogeneous curve-germs under the action of symplectomorphisms. We classify Lagrangian stars two to two transversal with respect to the group of simplectomorphisms. (AU)

• FAPESP's process: 12/16426-4 - Symplectic singularities of differentiable mappings
• Grantee: Fausto Assunção de Brito Lira
• Support Opportunities: Scholarships in Brazil - Doctorate