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Related Experiment Video

Updated: Jun 12, 2026

Experimental Methods to Study Human Postural Control

Experimental Methods to Study Human Postural Control

Published on: September 11, 2019

Snap-back repellers and chaotic attractors.

Laura Gardini¹, Fabio Tramontana

¹Department of Economics and Quantitative Methods, University of Urbino, Urbino, Italy. laura.gardini@uniurb.it

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

|May 21, 2010

Summary

This summary is machine-generated.

Snap-back repellers, when present, can lead to robust chaotic attracting sets in two-dimensional maps. This study explores their association in both continuous and discontinuous piecewise-linear maps.

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Area of Science:

Dynamical Systems and Chaos Theory
Nonlinear Dynamics
Mathematical Physics

Background:

Snap-back repellers are points in dynamical systems where homoclinic orbits exist.
These repellers are known to generate complex system behaviors.
Understanding their role is crucial for characterizing chaos.

Purpose of the Study:

To investigate the association between snap-back repellers and robust chaotic attracting sets.
To analyze this phenomenon in two-dimensional piecewise-linear maps.
To examine both continuous and discontinuous map forms.

Main Methods:

Analysis of two-dimensional piecewise-linear maps in canonical form.
Identification and characterization of homoclinic orbits.
Demonstration of snap-back repeller existence and behavior.

Main Results:

Snap-back repellers are demonstrated to be linked with robust chaotic attracting sets, not exclusively chaotic repellers.
Examples are provided for both continuous and discontinuous piecewise-linear maps.
The study confirms the broader role of snap-back repellers in generating complex dynamics.

Conclusions:

Snap-back repellers contribute to the formation of robust chaotic attracting sets in the studied map types.
The findings apply to both continuous and discontinuous piecewise-linear dynamical systems.
This research expands the understanding of chaos generation mechanisms in nonlinear systems.