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  1. No Access

    Article

    Birkhoff Program for Geodesic Flows of Surfaces and Applications: Homoclinics

    We show that a Kupka–Smale riemannian metric on a closed surface contains a finite primary set of closed geodesics, i.e. they intersect any other geodesic and divide the surface into simply connected regions. ...

    Gonzalo Contreras, Fernando Oliveira in Journal of Dynamics and Differential Equations (2024)

  2. No Access

    Article

    Existence of Birkhoff sections for Kupka–Smale Reeb flows of closed contact 3-manifolds

    A Reeb vector field satisfies the Kupka–Smale condition when all its closed orbits are non-degenerate, and the stable and unstable manifolds of its hyperbolic closed orbits intersect transversely. We show that...

    Gonzalo Contreras, Marco Mazzucchelli in Geometric and Functional Analysis (2022)

  3. No Access

    Article

    On Finite Quotient Aubry set for Generic Geodesic Flows

    We study the structure of the Mather and Aubry sets for the family of Lagrangians given by the kinetic energy associated to a Riemannian metric g on a closed manifold M. In this case the Euler-Lagrange flow is th...

    Gonzalo Contreras, José Antônio G. Miranda in Mathematical Physics, Analysis and Geometry (2020)

  4. No Access

    Article

    Ground states are generically a periodic orbit

    We prove that for an expanding transformation the maximizing measures of a generic Lipschitz function are supported on a single periodic orbit.

    Gonzalo Contreras in Inventiones mathematicae (2016)

  5. No Access

    Article

    Homogenization on arbitrary manifolds

    We describe a setting for homogenization of convex hamiltonians on abelian covers of any compact manifold. In this context we also provide a simple variational proof of standard homogenization results.

    Gonzalo Contreras, Renato Iturriaga… in Calculus of Variations and Partial Differe… (2015)

  6. No Access

    Article

    The Palais-Smale condition on contact type energy levels for convex Lagrangian systems

    We prove that for a uniformly convex Lagrangian system L on a compact manifold M, almost all energy levels contain a periodic orbit. We also prove that below Mañé's critical value of the lift of the Lagrangian to...

    Gonzalo Contreras in Calculus of Variations and Partial Differential Equations (2006)

  7. No Access

    Article

    Action potential and weak KAM solutions

    For convex superlinear lagrangians on a compact manifold M we characterize the Peierls barrier and the weak KAM solutions of the Hamilton-Jacobi equation, as defined by A. Fathi [9], in terms of their values at ...

    Gonzalo Contreras in Calculus of Variations and Partial Differential Equations (2001)

  8. No Access

    Article

    The hausdorff dimension of the harmonic class on negatively curved surfaces

    We study the regularity of the Hausdorff dimension of the harmonic class of a surface M of negative curvature as a function of the riemannian metric. We prove that it is a Cr− 3 function of the metric in the Bana...

    Gonzalo Contreras in The Journal of Geometric Analysis (1998)

  9. No Access

    Article

    Lagrangian flows: The dynamics of globally minimizing orbits-II

    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 Mañé's state...

    Gonzalo Contreras, Jorge Delgado… in Boletim da Sociedade Brasileira de Matemát… (1997)

  10. No Access

    Article

    Non-hyperbolic surfaces having all ideal triangles with finite area

    We construct examples ofC 3 compact surfaces of non-positive curvature having non-Anosov geodesic flows and satisfying the following property: there existsL>0 such that the area of every ideal triangle in the uni...

    Gonzalo Contreras, Rafael Oswaldo Ruggiero in Boletim da Sociedade Brasileira de Matemát… (1997)

  11. No Access

    Article

    The derivatives of equilibrium states

    We find some estimates for the derivatives of equilibrium states of subshifts of finite type. We prove the differentiability (with respect to the potential) of integrals of certain discontinuous functions for ...

    Gonzalo Contreras in Boletim da Sociedade Brasileira de Matemát… (1995)

  12. No Access

    Article

    Regularity of topological and metric entropy of hyperbolic flows

    Gonzalo Contreras in Mathematische Zeitschrift (1992)