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Doctoral Thesis
DOI
https://doi.org/10.11606/T.55.2017.tde-05082015-091649
Document
Author
Full name
Fausto Assunção de Brito Lira
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2015
Supervisor
Committee
Atique, Roberta Godoi Wik (President)
Costa, João Carlos Ferreira
Craizer, Marcos
Hefez, Abramo
Saia, Marcelo José
Title in Portuguese
Classificação simplética de germes de curvas parametrizadas e estrelas lagrangianas
Keywords in Portuguese
Classificação simplética
Estrelas lagrangianas
Método das restrições algébricas
Parte de quase grau mínimo proporcional
Abstract in Portuguese
Este trabalho tem como objetivo a classificação simplética de germes de curvas parametrizadas e de estrelas lagrangianas por meio do método das restrições algébricas. Classificamos simpleticamente germes de curvas parametrizadas com semigrupos (4; 5; 6); (4; 5; 7) e (4; 5; 6; 7). Introduzimos um invariante para distinguir restrições algébricas a germes de curvas parametrizadas quase homogêneas: a parte de quase grau mínimo proporcional. Através do método das restrições algébricas, este invariante é capaz de distinguir diferentes órbitas de germes de curvas parametrizadas quase homogêneas sob a ação dos germes de simplectomorfismos. Classificamos estrelas lagrangianas duas a duas transversais com respeito ao grupo dos simplectomorfismos.
Title in English
Symplectic classification of parameterized curve-germs and Lagrangian stars
Keywords in English
Lagrangian stars
Method of algebraic constraints
Symplectic classification
Abstract in English
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.
 
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Publishing Date
2017-08-25
 
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