FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1519287860> ?p ?o ?g. }

• W1519287860 endingPage "1239" @default.
• W1519287860 startingPage "1231" @default.
• W1519287860 abstract "We consider the problem of existence of fixed points of a continuous map <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f colon upper X right-arrow upper X> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>:</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mi>X</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>f:Xto X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in (possibly) noninvariant subsets. A pair <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis upper C comma upper E right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>C</mml:mi> <mml:mo>,</mml:mo> <mml:mi>E</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(C,E)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of subsets of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> induces a map <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f Superscript dagger Baseline colon upper C slash upper E right-arrow upper C slash upper E> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>f</mml:mi> <mml:mo>†<!-- † --></mml:mo> </mml:msup> <mml:mo>:</mml:mo> <mml:mi>C</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>E</mml:mi> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mi>C</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>E</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>f^dagger :C/Eto C/E</mml:annotation> </mml:semantics> </mml:math> </inline-formula> given by <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f Superscript dagger Baseline left-parenthesis left-bracket x right-bracket right-parenthesis equals left-bracket f left-parenthesis x right-parenthesis right-bracket> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>f</mml:mi> <mml:mo>†<!-- † --></mml:mo> </mml:msup> <mml:mo stretchy=false>(</mml:mo> <mml:mo stretchy=false>[</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=false>]</mml:mo> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=</mml:mo> <mml:mo stretchy=false>[</mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo stretchy=false>]</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>f^dagger ([x])=[f(x)]</mml:annotation> </mml:semantics> </mml:math> </inline-formula> if <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=x comma f left-parenthesis x right-parenthesis element-of upper C minus upper E> <mml:semantics> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>∈<!-- ∈ --></mml:mo> <mml:mi>C</mml:mi> <mml:mo class=MJX-variant>∖<!-- ∖ --></mml:mo> <mml:mi>E</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>x,f(x)in Csetminus E</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f Superscript dagger Baseline left-parenthesis left-bracket x right-bracket right-parenthesis equals left-bracket upper E right-bracket> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>f</mml:mi> <mml:mo>†<!-- † --></mml:mo> </mml:msup> <mml:mo stretchy=false>(</mml:mo> <mml:mo stretchy=false>[</mml:mo> <mml:mi>x</mml:mi> <mml:mo stretchy=false>]</mml:mo> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=</mml:mo> <mml:mo stretchy=false>[</mml:mo> <mml:mi>E</mml:mi> <mml:mo stretchy=false>]</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>f^dagger ([x])=[E]</mml:annotation> </mml:semantics> </mml:math> </inline-formula> elsewhere. The following generalization of the Lefschetz fixed point theorem is proved: <italic>If <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is metrizable, <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper C> <mml:semantics> <mml:mi>C</mml:mi> <mml:annotation encoding=application/x-tex>C</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E> <mml:semantics> <mml:mi>E</mml:mi> <mml:annotation encoding=application/x-tex>E</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are compact ANRs, and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f Superscript dagger> <mml:semantics> <mml:msup> <mml:mi>f</mml:mi> <mml:mo>†<!-- † --></mml:mo> </mml:msup> <mml:annotation encoding=application/x-tex>f^dagger</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is continuous, then <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding=application/x-tex>f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has a fixed point in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=ModifyingAbove upper C minus upper E With bar> <mml:semantics> <mml:mover> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo class=MJX-variant>∖<!-- ∖ --></mml:mo> <mml:mi>E</mml:mi> </mml:mrow> <mml:mo accent=false>¯<!-- ¯ --></mml:mo> </mml:mover> <mml:annotation encoding=application/x-tex>overline {Csetminus E}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> provided the Lefschetz number of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=ModifyingAbove upper H With tilde Superscript asterisk Baseline left-parenthesis f Superscript dagger Baseline right-parenthesis> <mml:semantics> <mml:mrow> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mi>H</mml:mi> <mml:mo>~<!-- ~ --></mml:mo> </mml:mover> </mml:mrow> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:msup> <mml:mo stretchy=false>(</mml:mo> <mml:msup> <mml:mi>f</mml:mi> <mml:mo>†<!-- † --></mml:mo> </mml:msup> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>widetilde H^ast (f^dagger )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is nonzero.</italic> Actually, we prove an extension of that theorem to the case of a composition of maps. We apply it to a result on the existence of an invariant set of a homeomorphism such that the dynamics restricted to that set is chaotic." @default.
• W1519287860 created "2016-06-24" @default.
• W1519287860 creator A5084276480 @default.
• W1519287860 date "1999-10-18" @default.
• W1519287860 modified "2023-09-27" @default.
• W1519287860 title "A generalization of the Lefschetz fixed point theorem and detection of chaos" @default.
• W1519287860 cites W1556479720 @default.
• W1519287860 cites W1965788748 @default.
• W1519287860 cites W1995257337 @default.
• W1519287860 cites W2018960775 @default.
• W1519287860 cites W2082172869 @default.
• W1519287860 cites W2091751087 @default.
• W1519287860 cites W2112602754 @default.
• W1519287860 cites W2596598149 @default.
• W1519287860 doi "https://doi.org/10.1090/s0002-9939-99-05467-2" @default.
• W1519287860 hasPublicationYear "1999" @default.
• W1519287860 type Work @default.
• W1519287860 sameAs 1519287860 @default.
• W1519287860 citedByCount "23" @default.
• W1519287860 countsByYear W15192878602014 @default.
• W1519287860 countsByYear W15192878602016 @default.
• W1519287860 countsByYear W15192878602023 @default.
• W1519287860 crossrefType "journal-article" @default.
• W1519287860 hasAuthorship W1519287860A5084276480 @default.
• W1519287860 hasBestOaLocation W15192878601 @default.
• W1519287860 hasConcept C11413529 @default.
• W1519287860 hasConcept C154945302 @default.
• W1519287860 hasConcept C18903297 @default.
• W1519287860 hasConcept C2776321320 @default.
• W1519287860 hasConcept C2777299769 @default.
• W1519287860 hasConcept C41008148 @default.
• W1519287860 hasConcept C86803240 @default.
• W1519287860 hasConceptScore W1519287860C11413529 @default.
• W1519287860 hasConceptScore W1519287860C154945302 @default.
• W1519287860 hasConceptScore W1519287860C18903297 @default.
• W1519287860 hasConceptScore W1519287860C2776321320 @default.
• W1519287860 hasConceptScore W1519287860C2777299769 @default.
• W1519287860 hasConceptScore W1519287860C41008148 @default.
• W1519287860 hasConceptScore W1519287860C86803240 @default.
• W1519287860 hasIssue "4" @default.
• W1519287860 hasLocation W15192878601 @default.
• W1519287860 hasLocation W15192878602 @default.
• W1519287860 hasOpenAccess W1519287860 @default.
• W1519287860 hasPrimaryLocation W15192878601 @default.
• W1519287860 hasRelatedWork W1529400504 @default.
• W1519287860 hasRelatedWork W1892467659 @default.
• W1519287860 hasRelatedWork W2143954309 @default.
• W1519287860 hasRelatedWork W2333703843 @default.
• W1519287860 hasRelatedWork W2334690443 @default.
• W1519287860 hasRelatedWork W2386767533 @default.
• W1519287860 hasRelatedWork W2394022102 @default.
• W1519287860 hasRelatedWork W2469937864 @default.
• W1519287860 hasRelatedWork W2808586768 @default.
• W1519287860 hasRelatedWork W2998403542 @default.
• W1519287860 hasVolume "128" @default.
• W1519287860 isParatext "false" @default.
• W1519287860 isRetracted "false" @default.
• W1519287860 magId "1519287860" @default.
• W1519287860 workType "article" @default.