Minimal solutions of monotone variational recurrence relations
Event details
| Date | 03.12.2014 |
| Hour | 16:30 › 17:30 |
| Speaker | Blaz Mramor (Freiburg) |
| Location |
GR A3 30
|
| Category | Conferences - Seminars |
Geometry and Dynamics Seminar
Abstract: Monotone variational recurrence relations arise in the study of Hamiltonian twist maps and in solid state physics, for example in the study of ferromagnetic crystals models. The existence and type of minimal solutions that such a recurrence relation admits, depends on the geometry of the underlying space. When the underlying space is a lattice, Aubry-Mather theory guarantees the existence of translation-invariant and ordered families of minimising solutions for every given mean lattice spacing. In the case of irrational lattice spacings, these give us the so-called Aubry-Mather sets, which are either connected families or Cantor sets of solutions. In case that the underlying space is a Cayley graph of a hyperbolic group, a richer family of uniformly bounded minimal solutions may be found.
Abstract: Monotone variational recurrence relations arise in the study of Hamiltonian twist maps and in solid state physics, for example in the study of ferromagnetic crystals models. The existence and type of minimal solutions that such a recurrence relation admits, depends on the geometry of the underlying space. When the underlying space is a lattice, Aubry-Mather theory guarantees the existence of translation-invariant and ordered families of minimising solutions for every given mean lattice spacing. In the case of irrational lattice spacings, these give us the so-called Aubry-Mather sets, which are either connected families or Cantor sets of solutions. In case that the underlying space is a Cayley graph of a hyperbolic group, a richer family of uniformly bounded minimal solutions may be found.
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- Sonja Hohloch