Helena Reis's Annual Report - 2014

Helena Reis's Annual Report - 2014

Year: 

2014

Brief description of the research activities: 

We studied the local dynamics of a subgroup of Diff(C2,0) possessing locally discrete orbits proving, in particular, that such subgroup must be virtually solvable. We also studied the structure of the recurrent set for more general groups. More precisely, given a non-solvable subgroup of Diff1(C2,0), we proved the existence of a neighbourhood U of the origin such that the set of points on U that fail to be recurrent has null Lebesgue mesure.

Study of the dynamics of non-solvable subgroups of Diff1(C2,0): basins of attraction and existence of vector fields whose flow is a limit of a sequence of elements of the group.

We showed that holomorphic vector fields on (C3,0) have separatrices provided that they are embedded in a rank 2 representation of a two-dimensional Lie algebra.

Projects description: 

Hamiltonian systems: from non-integrability to complex chaos, reference EXPL/MAT-CAL/1575/2013, funded by FCT (Fundação para a Ciência e Tecnologia)

Projects: 

Articles in international peer reviewed journals : 

Papers accepted for publication in peer reviewed journals: 

Helena Reis

Talks / Seminars / Courses : 

Title:
Orbites discrètes, récurrence et sous-groupes résolubles de Diff(C^2,0)
Name of the event:
Séminaire de Systèmes Dynamiques de Toulouse
Speakers
Helena Reis
Country:
France
Location / City:
Toulouse
Title:
Sobre o domínio de definição de soluções de campos de vectores uniformizáveis e algumas aplicações
Name of the event:
Seminário de Folheações Holomorfas
Speakers
Helena Reis
Country:
Brazil
Location / City:
IMPA
Title:
Aspectos topológicos de folheações completamente integráveis
Name of the event:
Seminário de Teoria das Folheações/Geometria Algébrica
Speakers
Helena Reis
Country:
Brazil
Location / City:
UFMG

Student Mentoring: 

Susana Pinheiro, Dynamics of holomorphic and stochastic differential equations, 2014

Work visits: 

- Institut de Mathématiques de Toulouse, France, January, 1-9 May, 1-15 September

- IMPA, Brazil, November-December