3 research outputs found
Compound orbits break-up in constituents: an algorithm
In this paper decomposition of periodic orbits in bifurcation diagrams are
derived in unidimensional dynamics system , being 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)
The Universal Cardinal Ordering of Fixed Points
We present the theorem which determines, by a permutation, the cardinal
ordering of fixed points for any orbit of a period doubling cascade. The
inverse permutation generates the orbit and the symbolic sequence of the orbit
is obtained as a corollary. The problem present in the symbolic sequences is
solved. There, repeated symbols appear, for example, the R (right), which
cannot be distinguished among them as it is not known which R is the rightmost
of them all. Therefore, there is a lack of information about the dynamical
system. Interestingly enough, it is important to point that this theorem needs
no previous information about any other orbit.Comment: 19 pages, 4 figure