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Hamiltonian Lattice Dynamical Systems
Hamiltonian lattice dynamical systems form a special but important class of models in the physical sciences. They arise naturally in the study of crystals in solid state physics, as many-particle models for statistical mechanics, as spatial discretisations of partial differential equations, modeling coupled oscillators in engineering and as idealizations of DNA molecules in the biological sciences. An important example of such a Hamiltonian lattice dynamical system is the Fermi- Pasta-Ulam chain, which was introduced 50 years ago. Its - at the time – surprising non-ergodicity properties strongly influenced the development of KAM theory, chaos and solitons. Our understanding of integrability and stochasticity in the Fermi-Pasta-Ulam chain is far from satisfactory, but recent progress on the role of symmetry, periodic and quasi-periodic behavior and integrable approximations is bound to lead to a better understanding of the process of energy equipartition and transport among vibrational excitations in lattice dynamical systems. In particular, the recent interest in nanoparticles and nanodevices, optical lattices and transport through molecules makes such an understanding highly desirable.
This workshop aims at bringing together two groups of researchers:
1. Mathematicians that work on lattice dynamical systems, in particular the Fermi-Pasta-Ulam problem, and related topics such as KAM theory, bifurcation theory and variational methods.
2. Physicists and numerical experimentalists with an interest in lattice dynamical systems and their applications.
Among the main topics to be addressed during this workshop are:
1. Integrability, near-integrability and KAM theory for Hamiltonian lattices.
2. Special solutions (solitary waves, rotating waves, breathers, etc.) and their bifurcations in a Hamiltonian framework.
3. Energy transport and ergodicity of Hamiltonian lattices.
4. Formal asymptotic methods and numerics.
Confirmed Invited Speakers are:
Serge Aubry (Saclay)