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Title: Is the Hénon attractor chaotic?

Abstract

By performing a systematic study of the Hénon map, we find low-period sinks for parameter values extremely close to the classical ones. This raises the question whether or not the well-known Hénon attractor—the attractor of the Hénon map existing for the classical parameter values—is a strange attractor, or simply a stable periodic orbit. Using results from our study, we conclude that even if the latter were true, it would be practically impossible to establish this by computing trajectories of the map.

Authors:
 [1];  [2]
  1. Department of Electrical Engineering, AGH University of Science and Technology, al. Mickiewicza 30, 30–059 Kraków (Poland)
  2. Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala (Sweden)
Publication Date:
OSTI Identifier:
22402534
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 3; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATTRACTORS; CHAOS THEORY; MAPPING; ORBITS; PERIODICITY; TRAJECTORIES

Citation Formats

Galias, Zbigniew, E-mail: galias@agh.edu.pl, and Tucker, Warwick, E-mail: warwick@math.uu.se. Is the Hénon attractor chaotic?. United States: N. p., 2015. Web. doi:10.1063/1.4913945.
Galias, Zbigniew, E-mail: galias@agh.edu.pl, & Tucker, Warwick, E-mail: warwick@math.uu.se. Is the Hénon attractor chaotic?. United States. doi:10.1063/1.4913945.
Galias, Zbigniew, E-mail: galias@agh.edu.pl, and Tucker, Warwick, E-mail: warwick@math.uu.se. Sun . "Is the Hénon attractor chaotic?". United States. doi:10.1063/1.4913945.
@article{osti_22402534,
title = {Is the Hénon attractor chaotic?},
author = {Galias, Zbigniew, E-mail: galias@agh.edu.pl and Tucker, Warwick, E-mail: warwick@math.uu.se},
abstractNote = {By performing a systematic study of the Hénon map, we find low-period sinks for parameter values extremely close to the classical ones. This raises the question whether or not the well-known Hénon attractor—the attractor of the Hénon map existing for the classical parameter values—is a strange attractor, or simply a stable periodic orbit. Using results from our study, we conclude that even if the latter were true, it would be practically impossible to establish this by computing trajectories of the map.},
doi = {10.1063/1.4913945},
journal = {Chaos (Woodbury, N. Y.)},
number = 3,
volume = 25,
place = {United States},
year = {Sun Mar 15 00:00:00 EDT 2015},
month = {Sun Mar 15 00:00:00 EDT 2015}
}