[Turkmath:7793] Viktor Ginzburg - IMBM

[ferit.ozturk at boun.edu.tr]

Istanbul Matematiksel Bilimler Merkezi Semineri


Conley Conjecture and Beyond: Infinitely Many Periodic Points of Hamiltonian
Dynamical Systems

Viktor Ginzburg
University of California, Santa Cruz

Abstract: 
One distinguishing feature of Hamiltonian dynamical systems is that such
systems,
with very few exceptions, tend to have numerous fixed and periodic points. In
1984
Conley conjectured that a Hamiltonian diffeomorphism (i.e., the time-one map of
a Hamiltonian flow) of a torus has infinitely many periodic points or, more
pre-
cisely, such a diffeomorphism with finitely many fixed points has simple
periodic
points of arbitrarily large period. This fact was proved by Hingston some
twenty
years later, in 2004. Similar results for Hamiltonian diffeomorphisms of
surfaces
of positive genus were also established by Franks and Handel. Of course, one
can
expect the Conley conjecture to to hold for a much broader class of closed
manifolds
and this is indeed the case. For instance, by now, the conjecture has been
proved
for the so-called closed, symplectically aspherical manifolds (including tori
and sur-
faces of positive genus) and the Calabi-Yau manifolds using symplectic
topological
techniques.
In this talk, mainly based on the results of Hein, Gurel and the speaker, we
will
examine underlying reasons for the existence of periodic orbits for Hamiltonian
flows
and maps and outline a proof of the Conley conjecture.

Date: Monday, July 4, 2011
Time: 14:00
Place: IMBM Seminar Room, Bogazici University

-------------- sonraki bölüm --------------
A non-text attachment was scrubbed...
Name: 4.7.11-ginzburg.pdf
Type: application/pdf
Size: 62030 bytes
Desc: kullanılamıyor
URL: <http://yunus.listweb.bilkent.edu.tr/cgi-bin/mailman/private/turkmath/attachments/20110628/5fba48ce/attachment-0001.pdf>