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Results tagged with gt.geometric-topology
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user 30684
Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).
3
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Accepted
examples of surface diffeomorphism that exhibit heteroclinic bifurcation?
It cannot happen in a continuous time 2D system, simply due to uniqueness of ODE property. At least (2+1)-D is needed, i.e. this phenomenon can be seen in 2D maps derived from taking time-T sections o …
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1
vote
Good books on Geometric Theory of Dynamical Systems
I guess "Geometrical Methods in the Theory of Ordinary Differential Equations" by Arnold should be in the list too, although it doesn't satisfy the "purely" topological criteria.
8
votes
Proofs where higher dimension or cardinality actually enabled much simpler proof?
Not a single theorem per se, but in dynamical systems, it is often very useful to translate questions about properties of a continuous system $\dot{x}=f(x)$ or discrete-time system $x_{k+1}=f(x_k)$, w …