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user 5010
6
votes
Approximation of topological dynamical systems?
In general, dynamical properties of dynamical systems are often quite unstable. The Mandelbrot set makes one nice parameter: the base equation $z \mapsto z^2 + c$ is varies continuously with respect t …
- 10.1k
5
votes
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Connected components of space of maps between two manifolds
Any continuous map from M to N is homotopic to a smooth map, and if two smooth maps are homotopic, then they are also smoothly homotopic. (More generally, two homotopic functions are homotopic throug …
- 10.1k