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Is the Hénon attractor chaotic?
Zbigniew Galias1, Warwick Tucker2
1Department of Electrical Engineering, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland.
Chaos (Woodbury, N.Y.)
|April 3, 2015
Summary
Researchers discovered low-period sinks in the Hénon map near classical parameters. This challenges the nature of the Hénon attractor, suggesting it might be a stable orbit, though difficult to prove computationally.
Area of Science:
- Dynamical Systems
- Chaos Theory
- Mathematical Physics
Background:
- The Hénon map is a fundamental example in chaos theory.
- Its classical attractor is widely studied but its precise nature remains debated.
Purpose of the Study:
- To systematically investigate the parameter space of the Hénon map.
- To determine if the classical Hénon attractor is a strange attractor or a stable periodic orbit.
Main Methods:
- Systematic numerical study of the Hénon map.
- Analysis of parameter values near the classical regime.
Main Results:
- Discovery of low-period sinks for parameter values extremely close to classical ones.
- Implication that the classical Hénon attractor might be a stable periodic orbit.
Conclusions:
- The classical Hénon attractor's nature is questioned.
- Even if it's a stable orbit, computational proof is practically infeasible.
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