Differentiable Dynamical Systems¶
Smale, S. (1967). Differentiable Dynamical Systems. Bulletin of the American Mathematical Society, 73(6), 747-817.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Chaos
- In mathematics, chaos is studied through iterated maps (logistic map, Hénon map, baker's map), continuous chaotic systems (Lorenz, Rössler), the Smale (1967) horseshoe
This sourceGlobal structural-stability analysis and topological characterization of dynamical systems on manifolds; introduces the Smale horseshoe and symbolic-dynamics treatment of chaos.
- In mathematics, chaos is studied through iterated maps (logistic map, Hénon map, baker's map), continuous chaotic systems (Lorenz, Rössler), the Smale (1967) horseshoe
- Phase Space
- Dimensionality-reduction techniques (PCA, embedding theorems) help but do not fully substitute for high-dimensional geometric reasoning.
This sourceProvides global structural-stability analysis and topological characterization of dynamical systems on manifolds; addresses high-dimensional phase-space structure and horseshoe chaos.
- Dimensionality-reduction techniques (PCA, embedding theorems) help but do not fully substitute for high-dimensional geometric reasoning.
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