Detecting the symmetry of attractors

DOI10.1016/0167-2789(93)90198-AzbMath0783.58042OpenAlexW1990469723MaRDI QIDQ1312520

Michael Dellnitz, Martin Golubitsky, Ernest Barany

Publication date: 20 March 1994

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(93)90198-a

zbMATH Keywords

symmetrydynamical systemsattractornumerical computation

Mathematics Subject Classification ID

Related Items (19)

Complex dynamics near a Hopf bifurcation with symmetry: A parameter study ⋮ Detection of symmetry of attractors from observations. I: Theory ⋮ Detection of symmetry of attractors from observations. II: An experiment with S\(_4\) symmetry ⋮ Detecting symmetry breaking bifurcations in the system describing the dynamics of coupled arrays of Josephson junctions ⋮ Semi-invariants, equivariants and algorithms ⋮ Attractors with the Symmetry of the n-Cube ⋮ Groups and nonlinear dynamical systems: chaotic dynamics on the \(\text{SU}(2)\times\text{SU}(2)\) group ⋮ A formula for a symmetry detective ⋮ Observing the symmetry of attractors ⋮ Recurrence and symmetry of time series: application to transition detection ⋮ Parameter uncertainties in models of equivariant dynamical systems ⋮ Isotropy of angular frequencies and weak chimeras with broken symmetry ⋮ The structure of symmetric attractors ⋮ Statics and dynamics of magnetic vortices and of Nielsen–Olesen (Nambu) strings ⋮ Several methods usable in production systems prediction ⋮ Spatial period-multiplying instabilities of hexagonal Faraday waves ⋮ Equivariance identification using delay differential equations ⋮ Koopman operator and its approximations for systems with symmetries ⋮ \(n\)-dimensional chaotic attractors with crystallographic symmetry

Cites Work

• The structure of symmetric attractors
• Symmetry-increasing bifurcation of chaotic attractors
• Singularities and groups in bifurcation theory. Volume II
• Symmetry groups of attractors
• Polynomial irreducible tensors for point groups
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