58 citations · 287 across the 30 of their papers we have counts for
35 papers
Bumpy metric theorem in the sense of Man{é} for non-convex Hamiltonians
Shahriar Aslani, Patrick Bernard
We prove a bumpy metric theorem in the sense of Mañe for non-convex Hamiltonians that are satisfying a certain geometric property.
Normal form near orbit segments of convex Hamiltonian systems
Shahriar Aslani, Patrick Bernard
In the study of Hamiltonian systems on cotangent bundles, it is natural to perturb Hamiltoni-ans by adding potentials (functions depending only on the base point). This led to the…
Cauchy and uniform temporal functions of globally hyperbolic cone fields
Patrick Bernard, Stefan Suhr
We study a class of time functions called uniform temporal functions in the general context of globally hyperbolic closed cone fields. We prove some existence results for uniform t…
Smoothing causal functions
Patrick Bernard, Stefan Suhr
We describe, in the general setting of closed cone fields, the set of causal functions which can be approximated by smooth Lyapunov. We derive several consequences on causality the…
Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders
Patrick Bernard, K Kaloshin, K Zhang
We prove a form of Arnold diffusion in the a priori stable case. Let H0(p) + H1(, p, t), T n , p B n , t T = R/T be a nearly integrable system of arbitr…
Lyapounov Functions of closed Cone Fields: from Conley Theory to Time Functions
Patrick Bernard, Stefan Suhr
We propose a theory "a la Conley" for cone fields using a notion of relaxed orbits based on cone enlargements, in the spirit of space time geometry. We work in the setting of close…