Friday, August 11

Iteration Theory of Maslov-type Index with Applications to Nonlinear Hamiltonian Systems

4:00 PM-4:50 PM
Kaoli (Salon 5)
Chair: E. Norman Dancer, University of Sydney, NSW, Australia

The speaker will present a survey on the iteration theory of the Maslov-type index for symplectic matrix paths and its applications established in recent years. The survey will include characterization of splitting numbers, Bott-type formulae, precise iteration formulae, and various iteration inequalities. They are established based upon the understanding of algebraic and topological properties of symplectic matrix groups and their subsets. This theory generalizes those of R. Bott of 1956 for close geodesics and I. Ekeland of 1980's for convex Hamiltonian systems. Applications of this iteration theory to Hamiltonian systems include: multiplicity and ellipticity of closed characteristics on any convex compact hypersurfaces in R2n, existence of infinitely many periodic solutions of periodic Lagrangian systems on tori, and existence of periodic solutions of nonlinear Hamiltonian systems with prescribed minimal period. (Partially supported by the NNSF and MCSEC of China, the Qiu Shi Sci. and Tech. Foundation, and CEC of Tianjin.)

Yiming Long
Nankai Institute of Mathematics
Nankai University, People's Republic of China
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