Gábor Domokos

Symbolic dynamics of infinite depth: finding global invariants for BVPs

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.