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Related Experiment Video

Updated: Jun 12, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Chaotic Hamiltonian systems: survival probability.

V A Avetisov¹, S K Nechaev

¹NN Semenov Institute of Chemical Physics, Russian Academy of Sciences, 1199911 Moscow, Russia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 21, 2010

Summary

This study explores survival probability in the standard mapping dynamical system. We introduce ultrametric diffusion to explain power-law decay, estimating the exponent nu near the chaos border.

Area of Science:

Dynamical Systems and Chaos Theory
Statistical Physics
Nonlinear Dynamics

Background:

The area-preserving standard mapping is a fundamental model in nonlinear dynamics.
Survival probability P(t) in this system exhibits power-law decay, P(t) ~ t{-nu}.
Understanding the dynamics near the chaos border is crucial for characterizing system behavior.

Purpose of the Study:

To develop new semiphenomenological arguments for analyzing the standard mapping near chaos.
To map the complex dynamics to a simpler model of ultrametric diffusion.
To estimate the exponent nu governing the power-law decay of survival probability.

Main Methods:

Development of semiphenomenological arguments to approximate the dynamical system.
Mapping the system near the chaos border to ultrametric diffusion on a treelike space.

Related Experiment Videos

Last Updated: Jun 12, 2026

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Hierarchical organization of transition rates within the treelike space model.

Main Results:

The dynamical system near the chaos border can be effectively modeled as ultrametric diffusion.
An estimation of the exponent nu is derived as nu = ln(2) / ln(1 + r_g).
The calculated value of nu is approximately 1.44, where r_g is the critical rotation number.

Conclusions:

The study provides a novel framework for understanding survival probability in the standard mapping.
Ultrametric diffusion offers a powerful conceptual tool for analyzing complex dynamical systems.
The derived exponent nu offers quantitative insight into the decay rates near the chaos border.