Birkhoff coordinates for the Toda Lattice in the infinite limit
speaker: Alberto Maspero (Università di Milano)abstract: We prove estimates uniform in the number of particles on the domain of definition of the Birkhoff coordinates for the Toda lattice. In order to prove results uniform with the size of the chain we apply to the Toda lattice a Vey type theorem recently proved by Kuksin and Perelman. The use of Kuksin Perelman's theorem is based on the Lax pair formulation and on the corresponding spectral construction of the integral of motion. So the adaption of the method to the Toda lattice requires the extension to Jacobi matrixes of some methods introduced for the study of Sturm Liouville problems.
The development of such method lead naturally to the introduction of spaces of sequences similar to Sobolev spaces, and to the extension to the framework of discrete systems of the connection between the decay of the spectral gaps and the smoothness of the corresponding state. We also deduce invariance of the spaces of smooth states under the dynamics of the Toda lattice.
timetable:
Fri 18 Feb, 15:15 - 15:45, Aula Bianchi Scienze
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