On the \(C^ 1\Omega\)-stability conjecture

DOI10.1007/BF02698932zbMath0648.58019WikidataQ122902734 ScholiaQ122902734MaRDI QIDQ1105249

Jacob Palis

Publication date: 1988

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=PMIHES_1987__66__211_0

zbMATH Keywords

Axiom A\(\Omega\)-stabilitynonwandering set of a diffeomorphism

Mathematics Subject Classification ID

Related Items (26)

Hyperbolic sets that are not contained in a locally maximal one ⋮ Weak hyperbolic structures and robust properties of diffeomorphisms and flows ⋮ \(C^{0}\) transversality and shadowing properties ⋮ Hyperbolicity versus weak periodic orbits inside homoclinic classes ⋮ On decomposition of ambient surfaces admitting \(A\)-diffeomorphisms with non-trivial attractors and repellers ⋮ The topological stability of diffeomorphisms ⋮ Stability of orbit spaces of endomorphisms ⋮ Periodic orbits and chain-transitive sets of \(C^1\)-diffeomorphisms ⋮ New criteria for hyperbolicity based on periodic sets ⋮ Closing lemmas ⋮ Lectures on structural stability in dynamics ⋮ Topological classification of \(\Omega\)-stable flows on surfaces by means of effectively distinguishable multigraphs ⋮ Robust nonhyperbolic dynamics and heterodimensional cycles ⋮ Diffeomorphisms in ℱ¹(M) satisfy Axiom A ⋮ Weak measure expansivity of \(C^2\) dynamics ⋮ Local topological stability for diffeomorphisms ⋮ Abundance of hyperbolicity in the $C^1$ topology ⋮ Structural stability and symbolic image ⋮ Invariant probability measures and non-wandering sets for impulsive semiflows ⋮ Nonsingular star flows satisfy Axiom A and the no-cycle condition ⋮ Hölder stability for \(C^r\) central translations ⋮ Vector fields in the interior of Kupka-Smale systems satisfy Axiom A. ⋮ The star systems \({\mathcal H}^*\) and a proof of the \(C^1 \Omega\)-stability conjecture for flows ⋮ Surface basic sets with wildly embedded supporting surfaces ⋮ Morse-Smale systems and horseshoes for three dimensional singular flows ⋮ Hyperbolicity in the volume-preserving scenario

Cites Work

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