Ergodic transport theory and piecewise analytic subactions for analytic dynamics

Piecewise Analytic Subactions for Analytic Dynamics

We consider a piecewise analytic expanding map f : [0, 1] → [0, 1] of degree d which preserves orientation, and an analytic positive potential g : [0, 1] → R. We address the analysis of the following problem: for a given analytic potential β log g, where β is a real constant, it is well known that there exists a real analytic (with a complex analytic extension to a small complex neighborhood of...

ar X iv : 0 90 4 . 35 16 v 1 [ m at h . D S ] 2 2 A pr 2 00 9 PIECEWISE ANALYTIC SUBACTIONS FOR ANALYTIC DYNAMICS

We consider a piecewise analytic expanding map f : [0, 1] → [0, 1] of degree d which preserves orientation, and an analytic positive potential g : [0, 1] → R. We address the analysis of the following problem: for a given analytic potential β log g, where β is a real constant, it is well known that there exists a real analytic (with a complex analytic extension to a small complex neighborhood of...

Zeros of real analytic ergodic Laplace eigenfunctions

Anisotropy and interference in wave transport: an analytic theory.

A theory is presented which incorporates the effect of dielectric anisotropy in random multiple scattering media. It predicts anisotropic diffusion, and a deflection of the diffuse energy flow in anisotropic slabs in the direction parallel to the slab. The transmittance integrated over all incoming and outgoing directions scales with the transport mean free path along the surface normal. The es...

Discrete dynamics versus analytic dynamics.

For discrete classical Molecular dynamics obtained by the "Verlet" algorithm (VA) with the time increment h there exists a shadow Hamiltonian H̃ with energy Ẽ(h), for which the discrete particle positions lie on the analytic trajectories for H̃. Here, we proof that there, independent of such an analytic analogy, exists an exact hidden energy invariance E(*) for VA dynamics. The fact that the disc...