CENTER FOR APPLIED MATHEMATICS AND THEORETICAL PHYSICS

UNIVERZA V MARIBORU UNIVERSITY OF MARIBOR

KREKOVA 2 SI-2000 MARIBOR SLOVENIA

Phone +(386) (2) 2355 350 and 2355 351 Fax +(386) (2) 2355 360

Robnik@uni-mb.si www.camtp.uni-mb.si

PROF.DR. MARKO ROBNIK, DIRECTOR

**Abstract:**
Studying formally gradient dynamics of the action functional of a
Hamiltonian system has its own merit. For example, for area-preserving twist
diffeomorphisms, we study dissipative dynamics of Frenkel-Kontorova models,
key models in solid-state physics. Arnoldâ€™s example of diffusion is associated
to a deceptively simple-looking reaction-diffusion equation. Formally gradient
dynamics has already been used to construct accelerating orbits, and invariant
measures supported on accelerating orbits of Hamiltonian systems with 1 1/2
degrees of freedom [4], [5], [6]. Recently, a number of new tools to study
formally gradient dynamics has been developed, related to the local energy flow,
motivated by examples such as the Navier-Stokes equation, and some chemical
reaction-diffusion equations [1], [2], [3], [7]. We outline an approach to apply
these tools to construction of accelerating orbits of Hamiltonian systems.

**Seminarsko predavanje bo v sredo 12. novembra 2014 ob 15:15 uri
v seminarski sobi CAMTP, Krekova 2, pritličje desno.
Vljudno vabljeni vsi zainteresirani, tudi
študentje.**

Prof.Dr. Marko Robnik

-- Direktor**CAMTP** --

-- Direktor