Differentiable dynamical systems

DOI10.1090/S0002-9904-1967-11798-1zbMath0202.55202OpenAlexW4212928962WikidataQ55878848 ScholiaQ55878848MaRDI QIDQ5601337

Stephen Smale

Publication date: 1967

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9904-1967-11798-1

Mathematics Subject Classification ID

Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Smooth dynamical systems: general theory (37Cxx)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geodesic flows on symmetric Riemann spaces
• Distral transformation groups
• Homogeneous vector bundles
• On the existence of slices for actions of non-compact Lie groups
• Structural stability on two-dimensional manifolds
• Generic one-parameter families of vector fields on two-dimensional manifolds
• Common singularities of commuting vector fields on 2-manifolds
• Structurally stable differential systems
• Lie algebra cohomology and the generalized Borel-Weil theorem
• Fixed point index and fixed point theorem for Euclidean neighborhood retracts
• On gradient dynamical systems
• Commuting vector fields on \(S^ 3\)
• Common periodic points of commuting functions
• Actions of \(R^ n\) on manifolds
• On an approximation theorem of Kupka and Smale
• Fixed points for iterates
• One-dimensional non-wandering sets
• Degeneracy of orbits of actions of \(R^ m\) on a manifold
• Structurally stable systems on open manifolds are never dense
• The extensibility of local Lie groups of transformations and groups on surfaces
• Real algebraic manifolds
• The existence of periodic points
• On the cohomology of compact homogeneous spaces of nilpotent Lie groups
• Measure-preserving homeomorphisms and metrical transitivity
• Geodesic flows on manifolds of constant negative curvature
• The maximal subgroups of the classical groups
• Local Contractions and a Theorem of Poincare
• On the Structure of Local Homeomorphisms of Euclidean n-Space, II
• Minimal sets: An introduction to topological dynamics
• Seminar on Transformation Groups. (AM-46)
• Morse inequalities for a dynamical system
• Equivalence of nearby differentiable actions of a compact group
• Deformations of Compact Differentiable Transformation Groups
• THE TOPOLOGY SUMMER INSTITUTE (Seattle, U.S.A., 1963)
• Topological Entropy
• The Construction of Minimal Discrete Flows
• Foliations and Pseudogroups
• On the Classification of Differentiable SO(n) Actions on Simply Connected π-Manifolds
• The Entropy of Chebyshev Polynomials
• Structurally Stable Systems are not Dense
• An Index of Fixed Point Type for Periodic Orbits
• The Formal Linearization of a Semisimple Lie Algebra of Vector Fields about a Singular Point
• The Closing Lemma
• An Improved Closing Lemma and a General Density Theorem
• Commuting Functions with No Common Fixed Point
• Remarks on Differentiable Actions of Non-Compact Semi-Simple Lie Groups on Euclidean Spaces
• Distal Affine Transformation Groups
• The Structure of Distal Flows
• The Structure of Local Homeomorphisms, III
• Energy Functions for Morse Smale Systems
• Homeomorphic conjugacy of automorphisms on the torus
• A Generalization of a Poincare-Bendixson Theorem to Closed Two-Dimensional Manifolds
• On the Asymptotic Behaviour of Solutions of a Differential Equation in Boundary Layer Theory
• A generalization of Morse-Smale inequalities
• Closed Integral Curves in 3-Space and Isotopic Two-Dimensional Deformations
• On the Discrete Subgroups and Homogeneous Spaces of Nilpotent Lie Groups
• On structural stability
• A second order differential equation with singular solutions