Compound orbits break-up in constituents: an algorithm

2014/02/24 by Jesús San Martín, A. González Gómez, Martín, Jesús San +5
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #nlin.CD

paper · pdf · doi:10.48550/arxiv.1402.5893

arxiv created 2014/02/24 · arxiv updated 2014/02/25

Abstract

In this paper decomposition of periodic orbits in bifurcation diagrams are derived in unidimensional dynamics system x_n+1=f(x_n;r), being f an unimodal function. We proof 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 (Physica D, 239:1135--1146, 2010).

Related

• On the bifurcation of periodic orbits
• Computational Bifurcation Analysis
• Period doubling in the Rossler system - a computer assisted proof
• The Period adding and incrementing bifurcations: from rotation theory to applications
• Periodic orbits near bifurcations of codimension two: Classical mechanics, semiclassics and Stokes transitions