For more information about this meeting, contact Dmitri Burago, Anatole Katok.
| Title: | Arnold diffusion for convex Hamiltonians in arbitrary degrees of freedom (joint with P. Bernard and K. Zhang). |
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| Seminar: | Center for Dynamics and Geometry Seminar |
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| Speaker: | Vadim Kaloshin, Penn State |
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| Abstract: |
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| Arnold in 60th conjectures that for generic nearly integrable Hamiltonian systems
H_\epsilon(\theta,p)=H_0(p)+\epsilon H_1(\theta,p,t), \theta \in T^n, p\in R^n,
t \in T there are orbits whose action changes by a magnitude of order of one:
\[
|p(t)-p(0)|=O(1) \text{ independently of how small epsilon is}.
\]
We solve a version of this conjecture for convex Hamiltonians, by showing
that for typical perturbations O(1) is indeed independent of epsilon, only
depends on H_1. In the proof we combine ideas from theory of normal
forms, Conley's isolating block, and Mather variational method.
This is a joint work with P. Bernard and K. Zhang. |
Room Reservation Information
| Room Number: | MB106 |
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| Date: | 02 / 07 / 2011 |
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| Time: | 03:35pm - 05:30pm |
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