Translation Arcs and Stability in Two Dimensions

DOI10.1007/978-3-662-52927-0_16zbMath1355.39009OpenAlexW2537665395MaRDI QIDQ2954214

Rafael Ortega

Publication date: 12 January 2017

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-662-52927-0_16

zbMATH Keywords

stabilityLyapunov stabilityvector fieldCantor setdegreediscrete systemtranslation arc

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Dynamics induced by flows and semiflows (37C10) Additive difference equations (39A10) Discrete version of topics in analysis (39A12)

Cites Work

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• On a generalization of the Schauder fixed point theorem
• An orbit closing proof of Brouwer's lemma on translation arcs
• Periodic solutions to two-dimensional forced systems: The Massera theorem and its extension
• The index of Lyapunov stable fixed points in two dimensions
• Existence of quasi-periodic orbits for twist homeomorphisms of the annulus
• The index of stable critical points
• Planar isolated and stable fixed points have index =1
• Limit periodic functions, adding machines, and solenoids
• Liapunov stability and adding machines revisited
• A new proof of the Brouwer plane translation theorem
• A fixed point theorem for plane homeomorphisms
• Shorter Notes: A Short Short Proof of the Cartwright-Littlewood Theorem
• The number of stable periodic solutions of time-dependent Hamiltonian systems with one degree of freedom
• Almost Periodic Flows and Solutions of Differential Equations
• Some fixed point theorems

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