Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders Bernard, Patrick Kaloshin, Vadim ; https://orcid.org/0000-0002-6051-2628 Zhang, Ke We prove a form of Arnold diffusion in the a-priori stable case. Let H0(p)+ϵH1(θ,p,t),θ∈Tn,p∈Bn,t∈T=R/T, be a nearly integrable system of arbitrary degrees of freedom n⩾2 with a strictly convex H0. We show that for a “generic” ϵH1, there exists an orbit (θ,p) satisfying ∥p(t)−p(0)∥>l(H1)>0, where l(H1) is independent of ϵ. The diffusion orbit travels along a codimension-1 resonance, and the only obstruction to our construction is a finite set of additional resonances. For the proof we use a combination of geometric and variational methods, and manage to adapt tools which have recently been developed in the a-priori unstable case. Institut Mittag-Leffler 2016 info:eu-repo/semantics/article doc-type:Article Article http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/8494 Bernard P, Kaloshin V, Zhang K. Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders. <i>Acta Mathematica</i>. 2016;217(1):1-79. doi:<a href="https://doi.org/10.1007/s11511-016-0141-5">10.1007/s11511-016-0141-5</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s11511-016-0141-5 info:eu-repo/semantics/altIdentifier/issn/0001-5962 info:eu-repo/semantics/closedAccess