Symmetric Attractors for Diffeomorphisms and Flows | Zendy

Field Michael | Zendy; Melbourne Ian | Zendy; Nicol Matthew | Zendy

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Symmetric Attractors for Diffeomorphisms and Flows

Author(s) -

Field Michael,

Melbourne Ian,

Nicol Matthew

Publication year - 1996

Publication title -

proceedings of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.899

H-Index - 65

eISSN - 1460-244X

pISSN - 0024-6115

DOI - 10.1112/plms/s3-72.3.657

Subject(s) - mathematics , equivariant map , attractor , invertible matrix , pure mathematics , symmetry (geometry) , axiom , group (periodic table) , reflection symmetry , diffeomorphism , symmetry group , dynamical systems theory , mathematical analysis , geometry , physics , quantum mechanics

Let Γ ⊂ O ( n ) be a finite group acting on R n . In this work we describe the possible symmetry groups that can occur for attractors of smooth (invertible) Γ‐equivariant dynamical systems. In case R n contains no reflection planes and n ⩾ 3, our results imply that there are no restrictions on symmetry groups. In case n ⩾ 4 (diffeomorphisms) and n ⩾ 5 (flows), we show that we may construct attractors which are Axiom A. We also give a complete description of what can happen in low dimensions.

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