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- Hypercyclic_operator abstract "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.The hypercyclicity is a special case of broader notions of topological transitivity (see topological mixing), and universality. Universality in general involves a set of mappings from one topological space to another (instead of a sequence of powers of a single operator mapping from X to X), but has a similar meaning to hypercyclicity. Examples of universal objects were discovered already in 1914 by Julius Pál, in 1935 by Józef Marcinkiewicz, or MacLane in 1952. However, it was not until the 1980s when hypercyclic operators started to be more intensively studied.".
- Hypercyclic_operator wikiPageID "26492417".
- Hypercyclic_operator wikiPageLength "4095".
- Hypercyclic_operator wikiPageOutDegree "21".
- Hypercyclic_operator wikiPageRevisionID "670803780".
- Hypercyclic_operator wikiPageWikiLink Banach_space.
- Hypercyclic_operator wikiPageWikiLink Bounded_linear_operator.
- Hypercyclic_operator wikiPageWikiLink Bounded_operator.
- Hypercyclic_operator wikiPageWikiLink Category:Functional_analysis.
- Hypercyclic_operator wikiPageWikiLink Category:Invariant_subspaces.
- Hypercyclic_operator wikiPageWikiLink Category:Operator_theory.
- Hypercyclic_operator wikiPageWikiLink Connectedness.
- Hypercyclic_operator wikiPageWikiLink Dense_set.
- Hypercyclic_operator wikiPageWikiLink Dimension_(vector_space).
- Hypercyclic_operator wikiPageWikiLink Functional_analysis.
- Hypercyclic_operator wikiPageWikiLink G_delta.
- Hypercyclic_operator wikiPageWikiLink Gδ_set.
- Hypercyclic_operator wikiPageWikiLink Invariant_subspace_problem.
- Hypercyclic_operator wikiPageWikiLink Józef_Marcinkiewicz.
- Hypercyclic_operator wikiPageWikiLink Lp_sequence_space.
- Hypercyclic_operator wikiPageWikiLink Lp_space.
- Hypercyclic_operator wikiPageWikiLink Mathematics.
- Hypercyclic_operator wikiPageWikiLink Mixing_(mathematics).
- Hypercyclic_operator wikiPageWikiLink Separable_space.
- Hypercyclic_operator wikiPageWikiLink Shift_operator.
- Hypercyclic_operator wikiPageWikiLink Topological_mixing.
- Hypercyclic_operator wikiPageWikiLink Topological_space.
- Hypercyclic_operator wikiPageWikiLink Vector_space.
- Hypercyclic_operator wikiPageWikiLinkText "Hypercyclic operator".
- Hypercyclic_operator wikiPageWikiLinkText "cyclic".
- Hypercyclic_operator wikiPageWikiLinkText "hypercyclic operator".
- Hypercyclic_operator authorlink "Charles Read".
- Hypercyclic_operator first "Charles".
- Hypercyclic_operator hasPhotoCollection Hypercyclic_operator.
- Hypercyclic_operator last "Read".
- Hypercyclic_operator wikiPageUsesTemplate Template:Citation.
- Hypercyclic_operator wikiPageUsesTemplate Template:Harvs.
- Hypercyclic_operator year "1988".
- Hypercyclic_operator subject Category:Functional_analysis.
- Hypercyclic_operator subject Category:Invariant_subspaces.
- Hypercyclic_operator subject Category:Operator_theory.
- Hypercyclic_operator hypernym T.
- Hypercyclic_operator type MartialArtist.
- Hypercyclic_operator type Function.
- Hypercyclic_operator type Physic.
- Hypercyclic_operator comment "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.".
- Hypercyclic_operator label "Hypercyclic operator".
- Hypercyclic_operator sameAs m.0bh7zmc.
- Hypercyclic_operator sameAs Гиперциклический_оператор.
- Hypercyclic_operator sameAs Q4138755.
- Hypercyclic_operator sameAs Q4138755.
- Hypercyclic_operator wasDerivedFrom Hypercyclic_operator?oldid=670803780.
- Hypercyclic_operator isPrimaryTopicOf Hypercyclic_operator.