Compound orbits break-up in constituents: An algorithm
Articles
Jesús San Martín
Technical University of Madrid, Spain
Antonia González Gómez
Techical University of Madrid, Spain
María José Moscoso
Techical University of Madrid, Spain
Daniel Rodriguez-Perez
National Distance Education University, Spain
Published 2015-01-20
https://doi.org/10.15388/NA.2015.1.8
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Keywords

visiting order permutation
next visiting permutation
decomposition theorem

How to Cite

San Martín J., Gómez A. G., Moscoso M. J. and Rodriguez-Perez D. (2015) “Compound orbits break-up in constituents: An algorithm”, Nonlinear Analysis: Modelling and Control, 20(1), pp. 112-131. doi: 10.15388/NA.2015.1.8.

Abstract

In this paper, decomposition of periodic orbits in bifurcation diagrams are derived in unidimensional dynamics system xn+1=f(xn;r), being f an unimodal function. We prove a theorem, which states the necessary and sufficient conditions for the break-up of compound orbits in their simpler constituents. A corollary to this theorem provides an algorithm for the computation of those orbits. This process closes the theoretical framework initiated in [J. San Martín, M.J. Moscoso, A. González Gómez, Composition law of cardinal ordering permutations, Physica D, 239:1135–1146, 2010. Theorem 2 of present work closes the theoretical frame of composition and decomposition.

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