NDLI: On lipschitz extension of interval maps

Content Provider	Springer Nature Link
Author	Bobok, Jozef
Copyright Year	2003
Abstract	Let [a, b] be a compact real interval andf: [a, b]→[a, b] a continuous map from [a, b] into itself. We say thatf is topologically mixing if for any openU, V⊂[a, b] there exists anN such thatf $^{ n }$ (U)∩V≠ϕ for anyn>N. Denote byA(f) the set of those from pointsa, b which have no preimages in (a, b) and ent(f) the topological entropy off. We show the following: Iff: [a, b]→[a, b] satisfies the conditions (i)f is topologically mixing, (ii)A(f)=ϕ, (iii) ent(f)=logν<∞, thenf has a ν-Lipschitz extension, i.e. there exist a ν-Lipschitz mapg: [a, b]→[a, b] and a nondecreasing surjective maph: [a, b]→[a, b] such thatf∘h=h∘g.
Starting Page	17
Ending Page	30
Page Count	14
File Format	PDF
ISSN	15755460
Journal	Qualitative Theory of Dynamical Systems
Volume Number	4
Issue Number	1
e-ISSN	16623592
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	2003-01-01
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Interval map topological mixing finite topological entropy Mathematics Dynamical Systems and Ergodic Theory Difference and Functional Equations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Discrete Mathematics and Combinatorics

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On lipschitz extension of interval maps