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Convex Hamiltonians without conjugate points

- G. Contreras, R. Iturriaga
- MathematicsErgodic Theory and Dynamical Systems
- 1 August 1999

We construct the Green bundles for an energy level without conjugate points of a convex Hamiltonian. In this case we give a formula for the metric entropy of the Liouville measure and prove that the… Expand

Convergence of the solutions of the discounted Hamilton–Jacobi equation

- A. Davini, A. Fathi, R. Iturriaga, M. Zavidovique
- Mathematics
- 28 August 2014

We consider a continuous coercive Hamiltonian H on the cotangent bundle of the compact connected manifold M which is convex in the momentum. If $$u_\lambda :M\rightarrow \mathbb {R}$$uλ:M→R is the… Expand

Burgers Turbulence and Random Lagrangian Systems

- R. Iturriaga, K. Khanin
- Mathematics
- 2003

Abstract: We consider a spatially periodic inviscid random forced Burgers equation in arbitrary dimension and the random time-dependent Lagrangian system related to it. We construct a unique… Expand

Physical solutions of the Hamilton-Jacobi equation

- N. Anantharaman, R. Iturriaga, P. Padilla, H. Sánchez-Morgado
- Mathematics
- 1 May 2005

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… Expand

Lagrangian flows: The dynamics of globally minimizing orbits-II

- G. Contreras, J. Delgado, R. Iturriaga
- Mathematics
- 1 September 1997

Define the critical levelc(L) of a convex superlinear LagragianL as the infimum of thek ∈ ℝsuch that the LagragianL+k has minimizers with fixed endpoints and free time interval. We provide proofs for… Expand

Convergence of the solutions of the discounted equation: the discrete case

- A. Davini, A. Fathi, R. Iturriaga, M. Zavidovique
- Mathematics
- 20 May 2016

We derive a discrete version of the results of Davini et al. (Convergence of the solutions of the discounted Hamilton–Jacobi equation. Invent Math, 2016). If M is a compact metric space, $$c :… Expand

Viscosity Limit of Stationary Distributions for the Random Forced Burgers Equation

- D. Gomes, R. Iturriaga, K. Khanin, P. Padilla
- Mathematics
- 2005

We prove convergence of stationary distributions for the randomly forced Burgers and Hamilton–Jacobi equations in the limit when viscosity tends to zero. It turns out that for all values of the… Expand

Hyperbolicity and exponential convergence of the Lax–Oleinik semigroup

- R. Iturriaga, H. Sánchez-Morgado
- Mathematics
- 1 March 2009

Lagrangian Graphs, Minimizing Measures and Mañé's Critical Values

- G. Contreras, R. Iturriaga, G. Paternain, M. Paternain
- Mathematics
- 1 November 1998

Abstract. Let
$\Bbb L$ be a convex superlinear Lagrangian on a closed connected manifold N. We consider critical values of Lagrangians as defined by R. Mañé in [M3]. We show that the critical value… Expand

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