Arnold diffusion in nearly integrable Hamiltonian systems of arbitrary degrees of freedom

Abstract

In this paper Arnold diffusion is proved to be a generic phenomenon in nearly integrable convex Hamiltonian systems with arbitrarily many degrees of freedom: $$ H(x,y)=h(y)+\eps P(x,y), \qquad x\in\mathbb{T}^n,\ y\in\mathbb{R}^n,\quad n\geq 3. $$ Under typical perturbation $\eps P$, the system admits "connecting" orbit that passes through any finitely many prescribed small balls in the same energy level $H^{-1}(E)$ provided $E>\min h$.

87 pages, 11 figures. Comments welcome! This is the solution of Arnold diffusion conjecture for convex Hamiltonians in the smooth category in the sense of cusp-residual genericity

References in corpus (7)

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Cited by in corpus (6)

• Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems
• Lasry-Lions, Lax-Oleinik and Generalized characteristics
• Arnold Diffusion, Quantitative Estimates and Stochastic Behavior in the Three-Body Problem
• A way to cross double resonance
• Arnold diffusion and geodesic dynamics of blackholes
• Arnold diffusion in multidimensional a priori unstable Hamiltonian systems