Local \(C^1\) stability versus global \(C^1\) unstability for iterative roots

DOI10.1016/j.jmaa.2011.07.045zbMath1368.65081OpenAlexW2318643415MaRDI QIDQ640944

Witold Jarczyk, Yingying Zeng, Wei Nian Zhang, WenMeng Zhang

Publication date: 21 October 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.07.045

zbMATH Keywords

stabilityperturbationiterative rootpulse

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (9)

On approximative embeddability of diffeomorphisms inC¹-flows ⋮ Iterative square roots of functions ⋮ Sharp regularity of linearization for \(C^{1,1}\) hyperbolic diffeomorphisms ⋮ Sharpness for \(C^1\) linearization of planar hyperbolic diffeomorphisms ⋮ Recent results on iteration theory: iteration groups and semigroups in the real case ⋮ Stability for iterative roots of piecewise monotonic functions ⋮ How violently do smooth iterative roots oscillate? ⋮ Local \(C^r\) stability for iterative roots of orientation-preserving self-mappings on the interval ⋮ Extension of iterative roots

Cites Work

• Continuity of iteration and approximation of iterative roots
• Construction of continuous solutions and stability for the polynomial-like iterative equation
• Finding iterative roots with a spiking neural network
• Fractional iterates for \(n\)-dimensional maps
• On functions with weak iterative roots
• A connection between fractional iteration and graph theory
• Iterative functional equation \(x(x(t))= f(t)\) with \(f(t)\) piecewise linear
• Computing iterative roots of polygonal functions
• A note on iterative roots of PM functions
• The Embedding of Homeomorphisms in Flows
• The inverse function theorem of Nash and Moser
• Vector fields generate few diffeomorphisms
• PM functions, their characteristic intervals and iterative roots
• On fractional iterates of a homeomorphism of the plane
• Recent results on functional equations in a single variable, perspectives and open problems
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