What is the effective impact of the explosive orbital growth in discrete-time one-dimensional polynomial dynamical systems?

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autor(en): Gallas J, Brison OJ
Zeitschrift: Physica A-Statistical Mechanics and Its Applications
Verlag: Elsevier
Jahr der Veröffentlichung: 2014
Band: 410
Seitenbereich: 313 - 318
ISSN: 0378-4371
Sprache: Englisch


Abstract


We study the distribution of periodic orbits in one-dimensional two-parameter maps. Specifically, we report an exact expression to quantify the growth of the number of periodic orbits for discrete-time dynamical systems governed by polynomial equations of motion of arbitrary degree. In addition, we compute high-resolution phase diagrams for quartic and for both normal forms of cubic dynamics and show that their stability phases emerge all distributed in a similar way, preserving a characteristic invariant ordering. Such coincidences are remarkable since our exact expression shows the total number of orbits of these systems to differ dramatically by more than several millions, even for quite low periods. All this seems to indicate that, surprisingly, the total number and the distribution of stable phases is not significantly affected by the specific nature of the nonlinearity present in the equations of motion.



FAU-Autoren / FAU-Herausgeber

Gallas, Jason Prof. Dr.
Lehrstuhl für Multiscale Simulation of Particulate Systems


Zusätzliche Organisationseinheit(en)
Exzellenz-Cluster Engineering of Advanced Materials


Autor(en) der externen Einrichtung(en)
University of Lisbon / Universidade de Lisboa (ULisboa)


Zitierweisen

APA:
Gallas, J., & Brison, O.J. (2014). What is the effective impact of the explosive orbital growth in discrete-time one-dimensional polynomial dynamical systems? Physica A-Statistical Mechanics and Its Applications, 410, 313 - 318. https://dx.doi.org/10.1016/j.physa.2014.05.049

MLA:
Gallas, Jason, and Owen J. Brison. "What is the effective impact of the explosive orbital growth in discrete-time one-dimensional polynomial dynamical systems?" Physica A-Statistical Mechanics and Its Applications 410 (2014): 313 - 318.

BibTeX: 

Zuletzt aktualisiert 2018-07-08 um 19:38