A counter-example to a C2 closing lemma

DOI10.1017/S0143385700004181zbMath0642.58036WikidataQ124944613 ScholiaQ124944613MaRDI QIDQ3784900

No author found.

Publication date: 1987

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

periodic pointbifurcation theorynon-wandering pointstability conjecture\(C^ 1\) ergodic closing lemma\(C^ r\)-connecting lemmaC\({}^ r\)-closing lemma

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)

Related Items (13)

On Peixoto’s conjecture for flows on non-orientable 2-manifolds ⋮ Stability properties of divergence-free vector fields ⋮ Peixoto Classification of 2-Dim Flows Revisited ⋮ Area-preserving surface diffeomorphisms ⋮ On the closing lemma for planar piecewise smooth vector fields ⋮ Closing lemmas ⋮ \(C^r\)-closing lemma for partially hyperbolic diffeomorphisms with 1D-center bundle ⋮ On the first integral conjecture of René Thom ⋮ Qualitative theory of flows on surfaces (a review) ⋮ Strengthening the \(C^r\)-closing lemma for dynamical systems and foliations on the torus ⋮ On \(C^{r}\)-closing for flows on orientable and non-orientable 2-manifolds ⋮ Closing Aubry Sets I ⋮ Le «closing lemma» en topologie $C^1$

Cites Work

• Structural stability on two-dimensional manifolds
• Bifurcations and stability of families of diffeomorphisms
• Against the \(C^2\) closing lemma
• Planar homoclinic points
• An ergodic closing lemma
• Homoclinic points in conservative systems
• An Improved Closing Lemma and a General Density Theorem

This page was built for publication: A counter-example to a C² closing lemma