Abstract
Topological conjugacy and various concepts of structural stability are defined, motivated, and criticized. Two basic problems emerge: characterization of structural stability and classification up to topological conjugacy. Solutions to these problems are outlined for linear automorphisms and the general characterization problem is discussed. © 1972, American Mathematical Society. All Rights Reserved.
Author supplied keywords
- Absolute structural stability
- Adjoint representation
- Anosov diffeomorphism
- Axiom A
- Cascade
- Conjugacy selector
- Differentiable conjugacy
- Ergodic
- Essential spectrum
- Flow
- Hyperbolic invariant set
- Hyperbolic linear automorphism
- Hyperbolic toral automorphism
- In-set
- Infinitesimally ergodic
- Nonwandering set
- North pole-south pole map
- On-set
- Out-set
- P-hyperbolic
- Relative structural stability
- Selector
- Semistability
- Sobolev space
- Stable manifold
- Strong structural stability
- Strong transversality condition
- Structural stability
- Symplectic manifold
- Topological conjugacy
- Topological stability
- Twist stability
- Unstable manifold
- Weak axiom A
- Weak transversality condition
- Yin-Yang problem
- Ω-hyperbolic
Cite
CITATION STYLE
APA
Robbin, J. W. (1972). Topological conjugacy and structural stability for discrete dynamical systems. Bulletin of the American Mathematical Society, 78(6), 923–952. https://doi.org/10.1090/S0002-9904-1972-13058-1
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