Symmetric ω-limit sets for smooth Γ-equivariant dynamical systems with Γ0 Abelian

Nonlinearity

Volumn 10, Issue 6, 1997, Pages 1551-1567

  Melbourne, Ian ^a   Stewart, Ian ^b  

^a University of Houston   (United States)

^b UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039384553     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/10/6/007     Document Type: Article

References (32)

1. Alexander J C, Kan I, Yorke J A and You Z 1992 Riddled basins Int. J. Bif. Chaos 2 795-813
2. Ashwin P, Buescu J and Stewart I N 1994 Bubbling of attractors and synchronisation of oscillators Phys. Lett. A 193 126-39
3. Ashwin P. Chossat P and Stewart I N 1994 Transitivity of orbits of maps symmetric under compact Lie groups Chaos Soliton. Fract. 4 621-34
4. Ashwin P and Melbourne I 1994 Symmetry groups of attractors Arch. Ration. Mech. Anal. 126 59-78
5. Berend D and Bergelson V 1984 Ergodic and mixing sequences of transformations Ergod. Theor. Dynam. Syst. 4 353-66
6. Brin M I 1975 Topological transitivity of one class of dynamic systems and flows of frames on manifolds of negative curvature Funct. Anal. 9 8-16
7. Brin M I, Feldman J and Katok A 1981 Bernoulli diffeomorphisms and group extensions of dynamical systems with non-zero characteristic exponents Ann. Math. 113 159-79
8. Bröcker T and tom Dieck T 1985 Representations of Compact Lie Groups (Graduate Texts in Mathematics 98) (New York Springer)
9. Christensen J P R 1972 On sets of Haar measure zero in Ahelian Polish groups Israel J. Math. 13 255-60
10. Dellnitz M, Golubitsky M and Melbourne I 1992 Mechanisms of symmetry creation Bifurcation and Symmetry ISNM 104 ed E Allgower, K Böhmer and M Golubitsky (Basel: Birkhäuser) pp 99-109
11. Dellnitz M and Melbourne I 1995 A note on the shadowing lemma and symmetric periodic points Nonlinearity 8 1067-75
12. d x SO(3. ℝ) Preprint (Zurich: Forschungsinstitut für Mathematik ETH)
13. Field M J 1991 Local structure for equivariant dynamics Singularity Theory and its Applications (Lecture Notes in Mathematics 1463) part II, ed M Roberts and I Stewart (Berlin: Springer) pp 142-66
14. Field M J, Golubitsky M and Nicol M 1994 A note on symmetries of invariant sets with compact group actions Equadiff. 8 93-104
15. Field M J, Melbourne I and Nicol M 1996 Symmetric attractors for diffeomorphisms and flows Proc. London Math. Soc. 72 657-96
16. Field M J and Parry W 1997 Stable ergodicity of skew extensions by compact Lie groups University of Houston Preprint
17. Golubitsky M, Marsden J E and Schaeffer D G 1984 Bifurcation problems with hidden symmetries Partial Differential Equations and Dynamical Systems (Research Notes in Mathematics 101) ed W E Fitzgibbon III (San Francisco. CA: Pitman) pp 181-210
18. Golubitsky M, Stewart I N and Schaeffer D G 1988 Singularities and Groups in Bifurcation Theory (Appl. Math. Sci. 69) vol 2 (New York: Springer)
19. Hirsch M W, Pugh C C and Shub M 1977 Invariant Manifolds (Lecture Notes in Mathematics 583) (New York: Springer)
20. Hunt B R, Sauer T and Yorke J A 1992 Prevalence, a translation-invariant 'almost every' on infinitedimensional spaces Bull. Am. Math. Soc. 27 217-38
21. Hunt B R, Sauer T and Yorke J A 1993 Prevalence: an addendum Bull. Am. Math. Soc. 28 306-7
22. Jones R and Parry W 1972 Compact Abelian group extensions of dynamical systems II Compositio Math. 25 135-47
23. Krupa M 1990 Bifurcations of relative equilibria SIAM J. Appl. Math. 21 1453-86
24. Mackey G W 1966 Ergodic theory and virtual groups Math. Ann. 166 187-207
25. Mañé R 1987 Ergodic Theory and Differentiable Dynamics (New York: Springer)
26. Melbourne I 1995 Generalizations of a result on symmetry groups of attractors Pattern Formation: Symmetry Methods and Applications (Fields Inst. Commun. 5) ed J Chadam and W Langford (Providence, RI: American Mathematical Society)
27. Melbourne I 1994 Instantaneous symmetry and symmetry on average in the Couette-Taylor and Faraday experiments Dynamics, Bifurcations, Symmetry ed P Chossat (Dordrecht: Kluwer) pp 241-57
28. Melbourne I 1997 Compact group extensions of topologically transitive sets for smooth dynamical systems University of Houston Preprint
29. Melbourne I, Dellnitz M and Golubitsky M 1993 The structure of symmetric attractors Arch. Rational Mech. Anal. 123 75-98
30. Mycielski J 1992 Unsolved problems on the prevalence of ergodicity, instability and algebraic independence Ulam Quarterly 1 30-7
31. Nerurkar M G 1988 On the construction of smooth ergodic skew-products Ergod. Theor. Dynam. Syst. 8 311-26
32. Zimmer R J 1977 Random walks on compact groups and the existence of cocycles Israel J. Math 26 84-90