×
Pixton, Dennis

Planar homoclinic points. (English) Zbl 0506.58029

J. Differ. Equations 44, 365-382 (1982).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0506.58029

Cited in 23 Documents

MSC:

37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
28D10 One-parameter continuous families of measure-preserving transformations
37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion

Keywords:

nonwandering set; transversal homoclinic point; area-preserving diffeomorphism

Citations:

Zbl 0247.58007; Zbl 0275.58013; Zbl 0261.58002
Cite Review PDF
Full Text: DOI

References:

[1] Abraham, R.; Marsden, J., Foundations of Mechanics (1978), Benjamin/Cummings: Benjamin/Cummings Reading, Mass. · Zbl 0393.70001
[2] Abraham, R.; Robbin, J., (Transversal Mappings and Flows (1967), Benjamin: Benjamin New York) · Zbl 0171.44404
[3] Hartman, P., Ordinary Differential Equations (1973), Wiley: Wiley New York · Zbl 0125.32102
[4] Hirsch, M., Differential Topology, (Graduate Texts in Mathematics 33 (1976), Springer-Verlag: Springer-Verlag New York) · Zbl 0121.18004
[5] Hirsch, M.; Pugh, C., Stable manifolds and hyperbolic sets, (Global Analysis, Part I. Global Analysis, Part I, Proc. Symp. Pure Math. 14 (1970), Amer. Math. Soc.: Amer. Math. Soc. Providence, R.I.), 133-164 · Zbl 0215.53001
[6] Kuratowski, K., (Topology, Vol. 2 (1966), Academic Press: Academic Press New York) · Zbl 0158.40802
[7] Moser, J., Stable and Random Motions in Dynamical Systems, (Annals of Mathematics Studies 77 (1973), Princeton Univ. Press: Princeton Univ. Press Princeton, NJ) · Zbl 0271.70009
[8] Moser, J., Nonexistence of integrals for canonical systems of differential equations, Comm. Pure Appl. Math., 8, 409-436 (1955) · Zbl 0068.29402
[9] Newman, M. H.A., Elements of the Topology of Plane Sets of Points (1964), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0021.06704
[10] Palis, J., On Morse-Smale dynamical systems, Topology, 8, 385-405 (1969) · Zbl 0189.23902
[11] Pugh, C., An improved closing lemma and a general density theorem, Amer. J. Math., 89, 1010-1021 (1967) · Zbl 0167.21804
[12] Robinson, C., Closing stable and unstable manifolds on the two sphere, (Proc. Amer. Math. Soc., 41 (1973)), 299-303 · Zbl 0275.58013
[13] Robinson, C., Generic properties of conservative systems, Amer. J. Math., 92, 562-603 (1970) · Zbl 0212.56502
[14] Smale, S., Diffeomorphisms with many periodic points, (Differential and Combinatorial Topology (1965), Princeton Univ. Press: Princeton Univ. Press Princeton, NJ), 63-70 · Zbl 0142.41103
[15] Takens, F., Homoclinic points in conservative systems, Invent. Math., 18, 267-292 (1972) · Zbl 0247.58007
[16] Zehnder, E., Homoclinic points near elliptic fixed points, Comm. Pure Appl. Math., 26, 131-182 (1973) · Zbl 0261.58002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.