Topological Characterization of Deterministic Chaos: Enforcing Orientation Preservation

The determinism principle, which states that dynamical state completely determines future time evolution, is a keystone of nonlinear dynamics and chaos theory. Since it precludes that two state space trajectories intersect, it is a core ingredient of a topological analysis of chaos based on a knot-t...

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Bibliographische Detailangaben
Veröffentlicht in:	Philosophical Transactions: Mathematical, Physical and Engineering Sciences. - The Royal Society. - 366(2008), 1865, Seite 559-567
1. Verfasser:	Lefranc, Marc (VerfasserIn)
Weitere Verfasser:	Morant, Pierre-Emmanuel, Nizette, Michel
Format:	Online-Aufsatz
Sprache:	English
Veröffentlicht:	2008
Zugriff auf das übergeordnete Werk:	Philosophical Transactions: Mathematical, Physical and Engineering Sciences
Schlagworte:	Chaos Unstable periodic orbits Knot theory Topology Entropy Applied sciences Philosophy Physical sciences Mathematics Behavioral sciences Information science


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245	1	0	\|a Topological Characterization of Deterministic Chaos: Enforcing Orientation Preservation
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520			\|a The determinism principle, which states that dynamical state completely determines future time evolution, is a keystone of nonlinear dynamics and chaos theory. Since it precludes that two state space trajectories intersect, it is a core ingredient of a topological analysis of chaos based on a knot-theoretic characterization of unstable periodic orbits embedded in a strange attractor. However, knot theory can be applied only to three-dimensional systems. Still, determinism applies in any dimension. We propose an alternative framework in which this principle is enforced by constructing an orientation-preserving dynamics on triangulated surfaces and find that in three dimensions our approach numerically predicts the correct topological entropies for periodic orbits of the horseshoe map.
540			\|a Copyright 2007 The Royal Society
650		4	\|a Chaos
650		4	\|a Unstable periodic orbits
650		4	\|a Knot theory
650		4	\|a Topology
650		4	\|a Entropy
650		4	\|a Applied sciences \|x Systems science \|x Systems theory \|x Chaos theory
650		4	\|a Philosophy \|x Metaphysics \|x Etiology \|x Determinism
650		4	\|a Physical sciences \|x Astronomy \|x Astrophysics \|x Celestial mechanics \|x Orbits \|x Orbital motion \|x Periodic orbits
650		4	\|a Physical sciences \|x Physics \|x Thermodynamics \|x Thermodynamic properties \|x Entropy
650		4	\|a Mathematics \|x Pure mathematics \|x Topology
650		4	\|a Physical sciences \|x Physics \|x Mechanics \|x Classical mechanics \|x Kinematics \|x Trajectories
650		4	\|a Behavioral sciences \|x Leisure studies \|x Recreation \|x Sports \|x Equestrianism \|x Horse tack \|x Horseshoes
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Statistical physics \|x Dimensional analysis \|x Dimensionality \|x Abstract spaces \|x Topological spaces \|x Mathematical manifolds \|x Hypersurfaces
650		4	\|a Mathematics \|x Pure mathematics \|x Topology \|x Topological properties \|x Homeomorphism
650		4	\|a Information science \|x Data products \|x Datasets \|x Time series
650		4	\|a Applied sciences \|x Systems science \|x Systems theory \|x Chaos theory
650		4	\|a Philosophy \|x Metaphysics \|x Etiology \|x Determinism
650		4	\|a Physical sciences \|x Astronomy \|x Astrophysics \|x Celestial mechanics \|x Orbits \|x Orbital motion \|x Periodic orbits
650		4	\|a Physical sciences \|x Physics \|x Thermodynamics \|x Thermodynamic properties \|x Entropy
650		4	\|a Mathematics \|x Pure mathematics \|x Topology
650		4	\|a Physical sciences \|x Physics \|x Mechanics \|x Classical mechanics \|x Kinematics \|x Trajectories
650		4	\|a Behavioral sciences \|x Leisure studies \|x Recreation \|x Sports \|x Equestrianism \|x Horse tack \|x Horseshoes
650		4	\|a Mathematics \|x Applied mathematics \|x Statistics \|x Applied statistics \|x Statistical physics \|x Dimensional analysis \|x Dimensionality \|x Abstract spaces \|x Topological spaces \|x Mathematical manifolds \|x Hypersurfaces
650		4	\|a Mathematics \|x Pure mathematics \|x Topology \|x Topological properties \|x Homeomorphism
650		4	\|a Information science \|x Data products \|x Datasets \|x Time series
655		4	\|a research-article
700	1		\|a Morant, Pierre-Emmanuel \|e verfasserin \|4 aut
700	1		\|a Nizette, Michel \|e verfasserin \|4 aut
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773	1	8	\|g volume:366 \|g year:2008 \|g number:1865 \|g pages:559-567
856	4	0	\|u https://www.jstor.org/stable/25190704 \|3 Volltext
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