Families of whiskered tori for a-priori stable/unstable Hamiltonian systems and construction of unstable orbits.
Valdinoci, Enrico (2000)
Mathematical Physics Electronic Journal [electronic only]
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Valdinoci, Enrico (2000)
Mathematical Physics Electronic Journal [electronic only]
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Guzzo, M., Fassò, F., Benettin, G. (1998)
Mathematical Physics Electronic Journal [electronic only]
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Massimiliano Berti, Luca Biasco, Enrico Valdinoci (2004)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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We prove, under suitable non-resonance and non-degeneracy “twist” conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic invariant tori (of hamiltonian systems). We prove the applicability of this result to the spatial planetary three-body problem in the small eccentricity-inclination regime. Furthermore, we find other periodic orbits under some restrictions on the period...
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...
Konstantin Athanassopoulos (1987)
Mathematische Zeitschrift
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Jürgen Pöschel (1989)
Mathematische Zeitschrift
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H. Hofer, K. Wysocki (1990)
Mathematische Annalen
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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 is homotopic to a stable Hamiltonian structure which cannot be embedded in . Moreover, we derive a structure theorem...
de la Llave, R., Wayne, C.E. (2004)
Mathematical Physics Electronic Journal [electronic only]
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Boris Khesin (1993)
Recherche Coopérative sur Programme n°25
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A. Katok, D. Bernstein (1987)
Inventiones mathematicae
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Hana Lichardová (2000)
Archivum Mathematicum
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