Lindstedt series, ultraviolet divergences and Moser's theorem
Magnetic Schrödinger Operator: Geometry, Classical and Quantum Dynamics and Spectral Asymptotics
I study the Schrödinger operator with the strong magnetic field, considering links between geometry of magnetic field, classical and quantum dynamics associated with operator and spectral asymptotics. In particular, I will discuss the role of short periodic trajectories.
On Prigogine's approaches to irreversibility: a case study by the baker map.
On the classical and quantum evolution of lagrangian half-forms in phase space
On the zero-temperature or vanishing viscosity limit for certain Markov processes arising from Lagrangian dynamics
We study the zero-temperature limit for Gibbs measures associated to Frenkel–Kontorova models on . We prove that equilibrium states concentrate on configurations of minimal energy, and, in addition, must satisfy a variational principle involving metric entropy and Lyapunov exponents, a bit like in the Ruelle–Pesin inequality. Then we transpose the result to certain continuous-time stationary stochastic processes associated to the viscous Hamilton–Jacobi equation. As the viscosity vanishes, the...
Prolongation loop algebras for a solitonic system of equations.
Quantum cohomology of flag manifolds and quantum Toda lattices.
Random matrices and permutations, matrix integrals and integrable systems
Regular and chaotic regimes in scalar field cosmology.
Scaling properties of a hybrid Fermi-Ulam-bouncer model.
Staircase baker's map generates flaring-type time series.
The effect of radiation on the stochastic web.
The magnetic geodesic flow in a homogeneous field on the complex projective space.
Theoretical foundation for the discrete dynamics of physicochemical systems: Chaos, self-organization, time and space in complex systems.
Time in dynamical systems.
Toy quantum mechanics using hidden variables.
Using density matrices in classical dynamical systems
Vacuum energy as spectral geometry.
Точное решение модели трех связанных осцилляторов с штарковской нелинейностью