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About: Hypercyclic operator     Goto   Sponge   NotDistinct   Permalink

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Type: martial artistyago:Abstraction100002137yago:Attribute100024264yago:MathematicalSpace108001685yago:WikicatInvariantSubspacesyago:Set107999699yago:Space100028651yago:Subspace108004342 New Facet based on Instances of this Class

In mathematics, especially functional analysis, a hypercyclic operator on a Banach space X is a bounded linear operator T: X → X such that there is a vector x ∈ X such that the sequence {Tn x: n = 0, 1, 2, …} is dense in the whole space X. In other words, the smallest closed invariant subset containing x is the whole space. Such an x is then called hypercyclic vector. There is no hypercyclic operator in finite-dimensional spaces, but the property of hypercyclicity in spaces of infinite dimension is not a rare phenomenon: many operators are hypercyclic.