scholarly journals The Lagrangian Conley conjecture

2011 ◽  
pp. 189-246 ◽  
Author(s):  
Marco Mazzucchelli
Keyword(s):  
Conley Conjecture

scholarly journals Conley Conjecture Revisited

2017 ◽  
Vol 2019 (3) ◽  
pp. 761-798 ◽  
Author(s):  
Viktor L Ginzburg ◽  
Başak Z Gürel
Keyword(s):  
Conley Conjecture

scholarly journals The Conley conjecture

2010 ◽  
Vol 172 (2) ◽  
pp. 1129-1183 ◽  
Author(s):  
Viktor Ginzburg
Keyword(s):  
Conley Conjecture

scholarly journals On the Conley conjecture for Reeb flows

2015 ◽  
Vol 26 (07) ◽  
pp. 1550047 ◽  
Author(s):  
Viktor L. Ginzburg ◽  
Başak Z. Gürel ◽  
Leonardo Macarini
Keyword(s):  
Magnetic Field ◽  
Energy Level ◽  
Periodic Orbits ◽  
Geodesic Flow ◽  
Low Energy ◽  
Contact Manifolds ◽  
Reeb Flows ◽  
Circle Bundles ◽  
Conley Conjecture

In this paper, we prove the existence of infinitely many closed Reeb orbits for a certain class of contact manifolds. This result can be viewed as a contact analogue of the Hamiltonian Conley conjecture. The manifolds for which the contact Conley conjecture is established are the pre-quantization circle bundles with aspherical base. As an application, we prove that for a surface of genus at least two with a non-vanishing magnetic field, the twisted geodesic flow has infinitely many periodic orbits on every low energy level.

scholarly journals TOTALLY NON-COISOTROPIC DISPLACEMENT AND ITS APPLICATIONS TO HAMILTONIAN DYNAMICS

2008 ◽  
Vol 10 (06) ◽  
pp. 1103-1128 ◽  
Author(s):  
BAŞAK Z. GÜREL
Keyword(s):  
Existence Theorem ◽  
Symplectic Manifold ◽  
Hamiltonian Dynamics ◽  
Conley Conjecture ◽  
Coisotropic Submanifold ◽  
Hamiltonian Diffeomorphism

In this paper, we prove the Conley conjecture and the almost existence theorem in a neighborhood of a closed nowhere coisotropic submanifold under certain natural assumptions on the ambient symplectic manifold. Essential to the proofs is a displacement principle for such submanifolds. Namely, we show that a topologically displaceable nowhere coisotropic submanifold is also displaceable by a Hamiltonian diffeomorphism, partially extending the well-known non-Lagrangian displacement property.

scholarly journals Conley conjecture and local Floer homology

2018 ◽  
Vol 111 (6) ◽  
pp. 647-656 ◽  
Author(s):  
Erman Çineli
Keyword(s):  
Floer Homology ◽  
Conley Conjecture
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