On the trajectories of orbits, their period-doubling cascades and saddle-node bifurcation cascades

Cerrada, Lucia; Martín, Jesús San

doi:10.1016/j.physleta.2011.02.023

Search citation statements

Order By: Relevance

Paper Sections

Select...

Appendix2

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2011

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(2 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…R symbolic sequence. We follow the notation introduced in [16]. Let S l,r be a p-periodic orbit with the symbolic sequence S l,r = CRL l) .…”

Section: Appendixmentioning

confidence: 99%

See 1 more Smart Citation

Topological imprint for periodic orbits

Martín

Moscoso

Gómez

2011

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

The more self-crossing points an orbit has the more complex it is. We introduce the topological imprint to characterize crossing points and focus on the period-doubling cascade. The period-doubling cascade topological imprint determines the topological imprint for orbits in chaotic bands. In addition, there is a closer link between this concept and the braids studied by Lettelier et al (2000 J. Phys. A: Math. Gen. 33 1809–25).

show abstract

“…R symbolic sequence. We follow the notation introduced in [16]. Let S l,r be a p-periodic orbit with the symbolic sequence S l,r = CRL l) .…”

Section: Appendixmentioning

confidence: 99%

“…(i) The permutation associated with an S l,2k orbit is given by theorem 3(i) [16]; it follows from this permutation that (i1) The critical point (the maximum of f ) is at the position 2k + 1, because the image by f of a point located at the position 2k + 1 is the point located at position 1. So points with positions 1, 2, 3, .…”

Section: Appendixmentioning

confidence: 99%