A short review of phase transition in a chaotic system

We investigate the localization of invariant spanning curves for a family of two-dimensional area-preserving mappings described by the dynamical variables [Formula: see text] and [Formula: see text] by using Slater’s criterion. The Slater theorem says there are three different return times for an irrational translation over a circle in a given interval. The returning time, which measures the number of iterations a map needs to return to a given periodic or quasi periodic region, has three responses along an invariant spanning curve. They are related to a continued fraction expansion used in the translation and obey the Fibonacci sequence. The rotation numbers for such curves are related to a noble number, leading to a devil’s staircase structure. The behavior of the rotation number as a function of invariant spanning curves located by Slater’s criterion resulted in an expression of a power law in which the absolute value of the exponent is equal to the control parameter [Formula: see text] that controls the speed of the divergence of [Formula: see text] in the limit the action [Formula: see text] is sufficiently small.

show abstract

Application of the Slater criteria to localize invariant tori in Hamiltonian mappings

Huggler

Hermes

Leonel

2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

Special issue on current trends in computational and experimental techniques in nonlinear dynamics

Panayotaros

Lambruschini

2022

Eur. Phys. J. Spec. Top.

View full text Add to dashboard Cite

Chenciner Bifurcation Presenting a Further Degree of Degeneration

2022

View full text Add to dashboard Cite

Chenciner bifurcation appears for some two-dimensional systems with discrete time having two independent variables. Investigated here is a special case of degeneration where the implicit function theorem cannot be used around the origin, so a new approach is necessary. In this scenario, there are many more bifurcation diagrams than in the two non-degenerated cases. Several numerical simulations are presented.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

A short review of phase transition in a chaotic system

Cited by 3 publications

References 23 publications

Application of the Slater criteria to localize invariant tori in Hamiltonian mappings

Application of the Slater criteria to localize invariant tori in Hamiltonian mappings

Special issue on current trends in computational and experimental techniques in nonlinear dynamics

Chenciner Bifurcation Presenting a Further Degree of Degeneration

Contact Info

Product

Resources

About