Planar homoclinic points

DOI10.1016/0022-0396(82)90002-XzbMath0506.58029WikidataQ100320625 ScholiaQ100320625MaRDI QIDQ1836921

Dennis Pixton

Publication date: 1982

Published in: Journal of Differential Equations (Search for Journal in Brave)

zbMATH Keywords

nonwandering settransversal homoclinic pointarea-preserving diffeomorphism

Mathematics Subject Classification ID

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

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Convex billiards on convex spheres, On Peixoto’s conjecture for flows on non-orientable 2-manifolds, Centralizers of area preserving diffeomorphisms on 𝑆², Forcing theory for transverse trajectories of surface homeomorphisms, Systems of differential equations that are competitive or cooperative. VI: A localC^rClosing Lemma for 3-dimensional systems, Closing lemmas, On the creation of homoclinic points, Homoclinic points in symplectic and volume-preserving diffeomorphisms, Homotopically unbounded disks for generic surface diffeomorphisms, Birth of homoclinic intersections: a model for the central dynamics of partially hyperbolic systems, A counter-example to a C² closing lemma, On generic rotationless diffeomorphisms of the annulus, Applications of Mañé’s 𝐶² connecting lemma, Erratum to: ``Transitivity of generic semigroups of area-preserving surface diffeomorphisms, Homoclinic intersections for geodesic flows on convex spheres, Decay of correlations for billiards with flat points I: channel effects, Rotation numbers and instability sets, Prime ends rotation numbers and periodic points, Genericity of symplectic diffeomorphisms of \(S^2\) with positive topological entropy. A remark on: ``Planar homoclinic points by P. Dixon and ``On the generic existence of homoclinic points by F. Oliveira., 𝐶¹ Connecting Lemmas, The creation of homoclinic points of \(C^ 1\)-maps, Homoclinic orbits for area preserving diffeomorphisms of surfaces

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