Displaying similar documents to “Families of whiskered tori for a-priori stable/unstable Hamiltonian systems and construction of unstable orbits.”

Exponentially stable manifolds in the neighbourhood of elliptic equilibria

Antonio Giorgilli, Daniele Muraro (2006)

Bollettino dell'Unione Matematica Italiana

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We consider a Hamiltonian system in a neighbourhood of an elliptic equilibrium which is a minimum for the Hamiltonian. With appropriate non-resonance conditions we prove that in the neighbourhood of the equilibrium there exist low dimensional manifolds that are exponentially stable in Nekhoroshev’s sense. This generalizes the theorem of Lyapounov on the existence of periodic orbits. The result may be meaningful for, e.g., the dynamics of non-linear chains of the Fermi-Pasta-Ulam (FPU)...

First steps in stable Hamiltonian topology

Kai Cieliebak, Evgeny Volkov (2015)

Journal of the European Mathematical Society

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In this paper we study topological properties of stable Hamiltonian structures. In particular, we prove the following results in dimension three: The space of stable Hamiltonian structures modulo homotopy is discrete; stable Hamiltonian structures are generically Morse-Bott (i.e. all closed orbits are Bott nondegenerate) but not Morse; the standard contact structure on S 3 is homotopic to a stable Hamiltonian structure which cannot be embedded in ℝ 4 . Moreover, we derive a structure theorem...

Compactness for embedded pseudoholomorphic curves in 3-manifolds

Chris Wendl (2010)

Journal of the European Mathematical Society

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We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem [BEH+C03] by using intersection theory to show that degenerations of such sequences never give rise to multiple covers or nodes, so transversality is easily achieved. This has application to the theory of stable finite energy foliations introduced in [HWZ03], and also suggests...