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Abstracts for Symplectic Geometry Day

Alternatively have a look at the program.

Positive loops of contactomorphisms

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Speaker: 
Peter Albers
Affiliation: 
Münster
Date: 
Thu, 2014-12-11 14:00 - 15:00
Location: 
MPIM Lecture Hall
Parent event: 
Symplectic Geometry Day

In 2000 Eliashberg-Polterovich introduced the notion of positive contact isotopies and studied induced biinvariant partial orders on contactomorphism groups. In 2006 Eliashberg-Kim-Polterovich discovered a link to contact (non-)squeezing. At the core of these works are so-called (contractible) positive loops of contactomorphisms. Existence of or obstructions to (contractible) positive loops are difficult questions. In my talk I will explain basic notions and give simple examples illustrating these.

Global surfaces of section for the restricted three body problem

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Speaker: 
Urs Frauenfelder
Affiliation: 
Augsburg
Date: 
Thu, 2014-12-11 15:00 - 16:00
Location: 
MPIM Lecture Hall
Parent event: 
MPI-Oberseminar
Parent event: 
Symplectic Geometry Day

In the restricted three body problem one studies the motion of a massless body which is attracted by two massive bodies according to Newton's law of gravitation. Due to preservation of energy if the massless body moves in the plane spanned by the two massive objects its dynamics is described by a Hamiltonian flow on a three dimensional energy hypersurface in four dimensional phase space. A global surface of section is a gadget which stores the dynamics on a three dimensional energy hypersurface in an area preserving disk map.

Global symplectic methods in low dimensional Hamiltonian systems

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Speaker: 
Barney Bramham
Affiliation: 
Bochum
Date: 
Thu, 2014-12-11 16:30 - 17:30
Location: 
MPIM Lecture Hall

In the late 90's Hofer-Wysocki-Zehnder showed that certain 3-dimensional Hamiltonian energy surfaces admit a surprising geometric decomposition by surfaces transverse to the dynamics. Their approach used holomorphic curve methods from symplectic geometry. Independently in 2004 LeCalvez constructed objects of a similar flavour for 2-dimensional systems using entirely topological methods (in particular without pde's) and successfully applied these to the dynamics of surface homeomorphisms.

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