Vered Rom-Kedar, (The Weizmann Institute, Rehovot, Israel): Billiard like potentials - theory and applications

 What kind of of solutions do multi-dimensional nonlinear
Hamiltonian systems admit? This is a difficult open question,
especially when far from integrable systems are considered.
We develop a paradigm for studying this question for a class
of Hamiltonian systems : smooth mechanical systems with
potentials that may be decomposed to a sum of an integrable
part and of a steep potential part [1,2].

Three applications of this paradigm will be discussed:

1)The destruction of ergodicity in some multi-dimensional
smooth steep systems that limit to uniformly hyperbolic
multi-dimensional dispersing billiards and its relation
to the Boltzmann ergodic hypothesis [3].

2) Simple models for tri-atomic co-linear reactions and
other scattering systems [4,5].

3) Robust particles accelerators [6].

Referencies:

[1] A. Rapoport, V. Rom-Kedar and D. Turaev, *Approximating
multi-dimensional Hamiltonian flows by billiards,
<http://www.wisdom.weizmann.ac.il/~vered/publistorder/R26_cmp07.pdf>
Comm. Math. Phys., 272(3), 567-600, 2007.*

[2] M. Kloc and * V. Rom-Kedar, in preparation.

[3] A. Rapoport, V. Rom-Kedar and D. Turaev, *Stability in high
dimensional steep repelling potentials
<http://www.wisdom.weizmann.ac.il/~vered/publistorder/R28_cmp07.pdf>
Comm. Math. Phys., 279, 497-534, 2008.

[4]L. Lerman and V. Rom-Kedar, A saddle in a corner - model of
collinear chemical reactions, submitted, 2011.

[5] A. Rapoport and V. Rom-Kedar, *Chaotic scattering by steep
potentials*,
<http://www.wisdom.weizmann.ac.il/~vered/publistorder/R29_PRE08.pdf>
Phys. Rev E., *77*, 016207 (2008) .

[6] V. Gelfreich, V. Rom-Kedar, K. Shah, D. Turaev, Robust
exponential ac
<http://www.wisdom.weizmann.ac.il/~vered/PRL15.PDF>
celerators
<http://www.wisdom.weizmann.ac.il/~vered/PRL15.PDF>,
PRL 106, 074101, 2011
<http://prl.aps.org/abstract/PRL/v106/i7/e074101>.