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Failure of convergence of the Lax-Oleinik semi-group in the time-periodic case. (English) Zbl 0989.37035

Summary: For a time-independent Lagrangian, the so-called Lax-Oleinik semigroup converges with an arbitrary continuous function as initial condition. Using twist maps, the authors show that there is no such convergence for time-periodic Lagrangians.

MSC:

37E40 Dynamical aspects of twist maps
35B40 Asymptotic behavior of solutions to PDEs
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)
35B10 Periodic solutions to PDEs
35F20 Nonlinear first-order PDEs
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References:

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