R-torsion and zeta functions for analytic Anosov flows on
3-manifolds
We improve previous results relating R-torsion, for an acyclic representation
of the fundamental group, with a special value of the torsion zeta
function of an analytic Anosov flow on a 3-manifold.
By using the new techniques of Rugh and Fried we get rid of the unpleasent
assumptions about the regularity of the invariant foliations.
dvi file available
Del-bar torsion and compact orbits of Anosov actions on complex 3-manifolds
In analogy with work of Fried and Laederich we study the relation
between del-bar torsion of a compact complex 3-manifold and the
compact orbits of an Anosov holomorphic action on the manifold.
pdf file available.
On the creation of conjugate points for Hamiltonian systems
For a fixed Hamiltonian H on the cotangent bundle of a compact manifold M
and a fixed energy level e, we prove that the set of potentials
on M such that the Hamiltonian flow of H plus the potential is Anosov, is the
interior in the C^2 topology of the set of potentials such that the
flow has no conjugate points. postcript file
available.
Finsler Metrics and Action Potentials
We study the behavior of Mañé's action potential $\Phi_k$
associated to a convex superlinear Lagrangian, for $k$ bigger than
the critical value $c(L)$ .
We obtain growth estimates of the action potential as function of $k$.
We prove that the action potential can be written as
$\Phi_k(x,y)=D_F(x,y)+f(y)-f(x)$ where $f$ is a smooth function and
$D_F$ is the distance function associated to a Finsler metric.
dvi file available.
Reidemeister torsion and integrable Hamiltonian systems Let N be a 4-dimensional symplectic manifold and let H be a real function on N such that there is a Bott function f independent of H with {H,f}=0. We study the relation between Reidemeister torsion of compact energy levels M={H=const}, and the critical circles and gradient lines of f connecting critical submanifolds of f on M. pdf file available.
A Minimax Selector for a Class Of Hamiltonians on a
Cotangent Bundle
We construct a minimax selector for eventually quadratic hamiltonians
on cotangent bundles. We use it to give a relation between Hofer's
energy and Mather's action minimizing function. We also study the
local flatness of the set of twist maps.
pdf file available.
Weak solutions of the Hamilton Jacobi equation for
periodic Lagrangians
In this work we generalize to periodic Lagrangians several results
-originally stated for autonomous Lagrangians- including the existence
of a Mañé's critical value , its characterization in terms
of smooth subsolutions of the Hamilton Jacobi equation and
the existence of Fathi's weak KAM solutions.
pdf file available.
Physical solutions of the Hamilton Jacobi equation
We consider a Lagrangian system on the d-dimensional torus, and the
associated Hamilton-Jacobi
equation. Assuming that the Aubry set of the system consists in a finite
number of hyperbolic periodic orbits of the Euler-Lagrange flow, we
study the vanishing-viscosity limit,
from the viscous equation to the inviscid problem. Under suitable
assumptions, we show that
solutions of the viscous Hamilton-Jacobi equation converge to a unique
solution of the inviscid problem.
dvi file available.
Hector Sanchez