Nontwist non-Hamiltonian systems

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 73, Issue 5, 2006, Pages

  Altmann, E G ^a   Cristadoro, G ^a   Pazo D ^a  

^a MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; PARAMETER ESTIMATION; PARTICLE ACCELERATORS;

NON-HAMILTONIAN SYSTEMS; PARAMETER SPACE; SHEARLESS TORUS;

HAMILTONIANS;

EID: 33646347360     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.73.056201     Document Type: Article

References (35)

1. J. A. G. Roberts and G. R. W. Quispel, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(92)90163-T 216, 63 (1992).
2. A. Politi, G. L. Oppo, and R. Badii, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.33.4055 33, 4055 (1986).
3. K. Y. Tsang, R. E. Mirollo, S. H. Strogatz, and K. Wiesenfeld, Physica D PDNPDT 0167-2789 10.1016/0167-2789(91)90054-D 48, 102 (1991).
4. K. Y. Tsang, S. H. Strogatz, and K. Wiesenfeld, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.66.1094 66, 1094 (1991).
5. D. Topaj and A. Pikovsky, Physica D PDNPDT 0167-2789 10.1016/S0167- 2789(02)00536-5 170, 118 (2002).
6. V. Arnold, Mathematical Methods of Classical Mechanics (Springer, New York, 1978).
7. J. E. Howard and S. M. Hohs, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.29.418 29, 418 (1984);
8. J. E. Howard and J. Humpherys, Physica D PDNPDT 0167-2789 10.1016/0167-2789(94)00180-X 80, 256 (1995).
9. D. del Castillo-Negrete, J. M. Greene, and P. J. Morrison, Physica D PDNPDT 0167-2789 10.1016/0167-2789(95)00257-X 91, 1 (1996).
10. P. Morrison, Phys. Plasmas PHPAEN 1070-664X 10.1063/1.874062 7, 2279 (2000).
11. R. Balescu, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.58.3781 58, 3781 (1998);
12. W. Horton, Phys. Plasmas PHPAEN 1070-664X 10.1063/1.873110 5, 3910 (1998);
13. M. Roberto, E. C. da Silva, I. L. Caldas, and R. Viana, Phys. Plasmas PHPAEN 1070-664X 10.1063/1.1630318 11, 214 (2004).
14. E. Petrisor, J. H. Misguich, and D. Constaniescu, Chaos, Solitons Fractals CSFOEH 0960-0779 10.1016/S0960-0779(03)00076-6 18, 1085 (2003).
15. D. del Castillo-Negrete and P. J. Morrison, Phys. Fluids A PFADEB 0899-8213 10.1063/1.858639 5, 948 (1993).
16. G. Corso and F. B. Rizzato, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.58.8013 58, 8013 (1998).
17. A. Wurm, A. Apte, K. Fuchss, and P. Morrison, Chaos CHAOEH 1054-1500 10.1063/1.1915960 15, 023108 (2005).
18. D. del Castillo-Negrete, J. M. Greene, and P. J. Morrison, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(96)00200-X 100, 311 (1997).
19. S. Shinohara and Y. Aizawa, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.97.379 97, 379 (1997);
20. S. Shinohara and Y. Aizawa, Prog. Theor. Phys. PTPKAV 0033-068X 10.1143/PTP.100.219 100, 219 (1998).
21. S. Saitô, Y. Nomura, K. Hirose, and Y. Ichikawa, Chaos CHAOEH 1054-1500 10.1063/1.166225 7, 245 (1997).
22. E. Shuckburgh and P. Haynes, Phys. Fluids PHFLE6 1070-6631 10.1063/1.1610471 15, 3342 (2003).
23. G. Stagika and S. Ichtiaroglou, Celest. Mech. Dyn. Astron. CMDAEP 0923-2958 78, 151 (2000).
24. M. B. Sevryuk, Physica D PDNPDT 0167-2789 112, 132 (1998).
25. N. Slater, Proc. Cambridge Philos. Soc. PCPSA4 0068-6735 63, 1115 (1967).
26. A. Apte, A. Wurm, and P. Morrison, Chaos CHAOEH 1054-1500 10.1063/1.1555472 13, 421 (2003).
27. D. Gaidashev and H. Koch, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/17/5/008 17, 1713 (2004).
28. P. Rosenau and A. Pikovsky, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.174102 94, 174102 (2005).
29. O. V. Popovych, Y. L. Maistrenko, and P. A. Tass, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.065201 71, 065201 (2005).
30. A. Apte, R. de la Llave, and N. Petrov, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/18/3/013 18, 1173 (2005).
31. Actually, the reconnection will not occur exactly in a line in the two-parameter space but in a (very) thin region as discussed by A. Apte, R. de la Llave, and E. Petrisor, Chaos, Solitons Fractals CSFOEH 0960-0779 27, 1115 (2006).
32. A. Pikovsky (private communication).
33. A dissipative analogous of these reconnections switches the basins of attraction of two stable foci. See, e.g., J. P. Van der Weele and T. P. Valkering, Physica A PHYADX 0378-4371 10.1016/0378-4371(90)90216-F 169 42 (1990);
34. S. M. Soskin, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(02)00269-7 373 247 (2003).
35. Examples of nontwist singularities for high-dimensional sympletic maps are extensively studied in H. R. Dullin and J. D. Meiss, Chaos CHAOEH 1054-1500 10.1063/1.1529450 13 1 (2003).