Ferromagnetic crystals and the destruction of minimal foliations

CDSNS Colloquium
Monday, April 8, 2013 - 4:30pm
1 hour (actually 50 minutes)
Skiles 005
Vrije Universiteit Amsterdam
A classical result of Aubry and Mather states that Hamiltonian twist maps have orbits of all rotation numbers. Analogously, one can show that certain ferromagnetic crystal models admit ground states of every possible mean lattice spacing. In this talk, I will show that these ground states generically form Cantor sets, if their mean lattice spacing is an irrational number that is easy to approximate by rational numbers. This is joint work with Blaz Mramor.