k-symmetry and return maps of spacetime symmetric flows

Nonlinearity

Volumn 11, Issue 3, 1998, Pages 601-629

  Lamb, Jeroen S W ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3342934225     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/11/3/011     Document Type: Article

References (32)

1. Arnol'd V I, Afrajmovich V S, Il'yashenko Yu S and Shil'nikov L P 1994 Bifurcation theory Dynamical Systems (Encyclopedia of Mathematical Sciences 5) vol 5, ed V I Arnol'd (Berlin: Springer) pp 1-205
2. Braathen A and Lamb J S W 1998 Planar crystallographic reversing k-symmetry groups, in preparation
3. Brands H, Lamb J S W and Hoveijn I 1995 Periodic orbits in k-symmetric dynamical systems Physica D 84 460-75
4. Broer H W and Takens F 1989 Formally symmetric normal forms and genericity Dynamics Reported vol 2, ed U Kirchgraber and H O Walter (New York: Wiley) pp 39-59
5. Broer H W and Vegter G 1992 Bifurcational aspects of parametric resonance Dynamics Reported (New Series) vol 1, ed C K T R Jones, U Kirchgraber and H O Walter (Berlin: Springer) pp 1-53
6. Chossat P (ed) 1994 Dynamics, Bifurcation and Symmetry (NATO ASI Series C 437) (Dordrecht: Kluwer)
7. Fiedler B 1988 Global Bifurcations of Periodic Solutions with Symmetry (Lecture Notes in Mathematics 1309) (Berlin: Springer)
8. Field M, Melbourne I and Nicol M 1996 Symmetric attractors for diffeomorphisms and flows Proc. London Math. Soc. 72 657-96
9. Golubitsky M, Stewart I N and Schaeffer D G 1988 Singularities and Groups in Bifurcation Theory (Applied Mathematical Sciences 69) vol 2 (New York: Springer)
10. Hénon M 1969 Numerical study of quadratic area-preserving mappings Quart. Appl. Math. XXVII 291-312
11. Knobloch J and Vanderbauwhede A 1994 Hopf bifurcation at k-fold resonances in equivariant reversible systems Dynamics. Bifurcation and Symmetry (NATO ASI Series C 437) ed P Chossat (Dordrecht: Kluwer) pp 167-79
12. Krupa M 1990 Bifurcations of relative equilibria SIAM J. Math. Anal. 21 1453-86
13. Lamb J S W 1992 Reversing symmetries in dynamical systems J. Phys. A: Math. Gen. 25 925-37
14. Lamb J S W 1993 Crystallographic symmetries of stochastic webs J. Phys. A: Math. Gen. 26 2921-33
15. Lamb J S W 1994 Reversing symmetries in dynamical systems PhD Thesis University of Amsterdam
16. Lamb J S W 1995 Resonant driving and k-symmetry Phys. Lett. A 199 55-60
17. Lamb J S W 1996 Local bifurcations in k-symmetric dynamical systems Nonlinearity 9 537-57
18. Lamb J S W and Brands H 1994 Symmetries and reversing symmetries in kicked systems Dynamics, Bifurcation and Symmetry (NATO ASI Series C 437) ed P Chossat (Dordrecht: Kluwer) pp 181-96
19. Lamb J S W and Nicol M 1996 On symmetric ω-limit sets in reversible flows Nonlinear Dynamical Systems and Chaos (Progress in Nonlinear Differential Equations and Their Applications 19) ed H W Broer et al (Basel: Birkhäuser) pp 103-20
20. Lamb J S W and Quispel G R W 1994 Reversing k-symmetries in dynamical systems Physica D 73 277-304
21. Lamb J S W and Quispel G R W 1995 Cyclic reversing k-symmetry groups Nonlinearity 8 1005-26
22. Lamb J S W and Roberts J A G 1998 Time-reversal symmetry in dynamical systems: a survey Physica D 112 1-39
23. Nikolaev E V 1994 Periodic motions in systems with a finite symmetry group Preprint
24. Roberts J A G and Quispel G R W 1992 Chaos and time-reversal symmetry: order and chaos in reversible dynamical systems Phys. Rep. 216 63-177
25. Robinson C 1995 Dynamical Systems: Stability, Symbolic Dynamics and Chaos (Boca Raton, FL: Chemical Rubber Company)
26. Rucklidge A M and Silber M 1997 Instabilities of periodic solutions with spatiotemporal symmetries Preprint
27. Sevryuk M B 1986 Reversible Systems (Lecture Notes in Mathematics 1211) (Berlin: Springer)
28. Swift J W and Wiesenfeld K 1984 Suppression of period doubling in symmetric systems Phys. Rev. Lett. 52 705-8
29. Takens F 1974 Forced oscillations and bifurcations Applications of Global Analysis (Communications of the Mathematical Institute 1) (Ultrecht: Rijksuniversiteit) pp 1-59
30. Vanderbauwhede A 1990 Hopf bifurcation for equivariant conservative and time-reversible systems Proc. R. Soc. A 116 103-28
31. Vanderbauwhede A 1992 Branching of periodic solutions in time-reversible systems Geometry and Analysis in Nonlinear Dynamics (Pitman Res. Notes Math. 222) ed H W Broer and F Takens (Harlow: Longman) pp 97-113
32. Wiggins S 1990 Introduction to Applied Nonlinear Dynamical Systems and Chaos (Texts in Applied Mathematics 2) (New York: Springer)