A proof of the \(C^ 1\) stability conjecture

From MaRDI portal
Publication:1124188

DOI10.1007/BF02698931zbMath0678.58022OpenAlexW2314726047WikidataQ123166083 ScholiaQ123166083MaRDI QIDQ1124188

Ricardo Mañé

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__161_0




Related Items (only showing first 100 items - show all)

Classification of suspensions over cartesian products of orientation-reversing diffeomorphisms of a circleEventual shadowing for chain transitive sets of $C^1$ generic dynamical systemsUniform hyperbolicity revisited: index of periodic points and equidimensional cyclesTwo-dimensional attractors of A-flows and fibred links on three-manifoldsOn structurally stable diffeomorphisms with codimension one expanding attractorsLectures on structural stability in dynamicsThe entropy of 𝐶¹-diffeomorphisms without a dominated splittingBistable vector fields are axiom AOn the topological structure of manifolds supporting axiom a systemsMorse flows with fixed points on the boundary of 3-manifoldsSmale regular and chaotic A-homeomorphisms and A-diffeomorphismsUnnamed ItemUnnamed ItemAbundance of hyperbolicity in the $C^1$ topologyExpansive transitive sets for robust and generic diffeomorphismsPerturbations of normally hyperbolic manifolds with applications to the Navier-Stokes equationsStatistical properties of chaotic systemsLocal rigidity of actions of higher rank abelian groups and KAM methodVector fields in the interior of Kupka-Smale systems satisfy Axiom A.On the hyperbolicity of \(\operatorname{C}^1\)-generic homoclinic classesStable ergodicityRobust cycles unfolding from conservative bifocal homoclinic orbitsThe Topological Classification of Diffeomorphisms of the Two-Dimensional Torus with an Orientable AttractorOn interrelations between trivial and nontrivial basic sets of structurally stable diffeomorphisms of surfacesHyperbolic sets that are not contained in a locally maximal oneRobustly chain transitive diffeomorphismsClassification of Smale diffeomorphisms of surfaces: realisable geometric typesOn the topological classification of structurally stable diffeomorphisms on 3-manifolds with a 2-dimensional expanding attractorStructural stability of attractor–repellor endomorphisms with singularitiesWeak hyperbolic structures and robust properties of diffeomorphisms and flowsSHADOWING PROPERTIES OF RANDOM HYPERBOLIC SETSThe $C^1$ closing lemma for nonsingular endomorphisms equivariant under free actions of finite groupsUnnamed ItemRobust chain transitive vector fieldsConditions for dominated splittingsStability properties of divergence-free vector fields\(C^1\)-stably shadowable chain components are hyperbolicHyperbolicity versus weak periodic orbits inside homoclinic classesVector fields with the oriented shadowing propertyUnnamed ItemDynamical Systems with Nontrivially Recurrent Invariant ManifoldsSome Recent Results on the Stability of EndomorphismsFranks' lemma for \(C^2\)-Mañé perturbations of Riemannian metrics and applications to persistenceThe topological classification of structurally stable 3-diffeomorphisms with two-dimensional basic setsRandom perturbations and statistical properties of Hénon-like mapsSpecification and partial hyperbolicity for flowsStability of orbit spaces of endomorphismsRoutes to chaos in high-dimensional dynamical systems: a qualitative numerical studyA $C^2$ generic trichotomy for diffeomorphisms: Hyperbolicity or zero Lyapunov exponents or the $C^1$ creation of homoclinic bifurcationsPeriodic orbits and chain-transitive sets of \(C^1\)-diffeomorphismsNew criteria for hyperbolicity based on periodic setsClosing lemmasOn the number of heteroclinic curves of diffeomorphisms with surface dynamicsOn the \(C^{1}\) robust transitivity of the geometric Lorenz attractorRobust heteroclinic tangenciesThe centralizer of Komuro-expansive flows and expansive \({{\mathbb {R}}}^d\) actionsQuasiattractors and homoclinic tangencies\(p\)-dominant switched linear systemsFrontiers in complex dynamicsDominated splitting of differentiable dynamics with \(\mathrm{C}^1\)-topological weak-star propertyDiffeomorphisms in 1(M) satisfy Axiom ARough diffeomorphisms with basic sets of codimension oneStructural stability of the inverse limit of endomorphismsScenario of a simple transition from a structurally stable 3-diffeomorphism with a two-dimensional expanding attractor to a DA diffeomorphismDiffeomorphisms with pseudo orbit tracing propertyPositively measure-expansive differentiable mapsLocal rigidity of partially hyperbolic actions I. KAM method and \({\mathbb Z^k}\) actions on the torusA note on the shadowing lemma of Liao: a generalized and improved versionOn the notions of singular domination and (multi-)singular hyperbolicityOn \(\mathrm{C}^1\)-class local diffeomorphisms whose periodic points are nonuniformly expandingThree-color graph of the Morse flow on a compact surface with boundaryStrictly invariant sets for 2-D tent maps: 2-D strange attractorsEquivariant bifurcation theory and symmetry breakingSinks and sources for \(C^1\) dynamics whose Lyapunov exponents have constant signOn the inverse limit stability of endomorphismsPhysical measures and absolute continuity for one-dimensional center directionPeriodic orbits and expansivenessApplications of Mañé’s 𝐶² connecting lemmaEssential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphismsStructural stability and symbolic imageClimate dynamics and fluid mechanics: Natural variability and related uncertaintiesDominated splitting versus small anglesThe wind-driven ocean circulation: applying dynamical systems theory to a climate problemSURVEY Towards a global view of dynamical systems, for the C1-topologyCentralizers of Anosov diffeomorphisms on toriStructurally stable perturbations of polynomials in the Riemann sphereDiffeomorphisms with a generalized Lipschitz shadowing propertyLyapunov stability and sectional-hyperbolicity for higher-dimensional flowsA global perspective for non-conservative dynamicsHyperbolicity of \(C^{1}\)-star invariant sets for \(C^{1}\)-class dynamical systemsNonsingular star flows satisfy Axiom A and the no-cycle conditionPeriodically expansive homoclinic classesThe construction of an energy function for three-dimensional cascades with a two-dimensional expanding attractorHölder stability for \(C^r\) central translationsPartial hyperbolicity and specificationCodimension one structurally stable chain classesNecessary and Sufficient Conditions for HyperbolicitySingular robustly chain transitive sets are singular volume partial hyperbolicBeyond topological hyperbolicity: the L-shadowing propertyStar flows and multisingular hyperbolicity



Cites Work


This page was built for publication: A proof of the \(C^ 1\) stability conjecture