Symbolic dynamics of infinite depth: Finding global invariants for BVPs

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Abstract

Continuing the work of Domokos and Holmes [G. Domokos and P. Holmes, J. Nonlinear Sci. 3 (1993) 109-151] and Domokos [G. Domokos, Phil. Trans. Roy. Soc. Lond. A 355 (1997) 2099-2116], we explore global bifurcation diagrams of elastic linkages subject to quasi-static, conservative, one-parameter load. The main result is an explicit construction of a finite length, infinite depth symbolic dynamics which uniquely characterizes all solutions of the boundary value problem (BVP). We give an estimate based on global symmetry arguments that provides a powerful tool for the numerical identification of the symbolic dynamics. The same estimate is helpful to find self-similar distribution patterns for the stable solutions.

Original languageEnglish
Pages (from-to)316-336
Number of pages21
JournalPhysica D: Nonlinear Phenomena
Volume134
Issue number3
DOIs
Publication statusPublished - Nov 15 1999

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Keywords

  • Global invariant
  • Infinite depth
  • Symbolic dynamics

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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