Compound windows of the Hénon-map

Physica D: Nonlinear Phenomena

Volumn 237, Issue 13, 2008, Pages 1689-1704

  Lorenz, Edward N ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Bifurcation curves; Periodic windows; Two parameter maps

Indexed keywords

CHAOS THEORY; COMPUTATION THEORY; PARAMETER ESTIMATION; RANDOM PROCESSES;

BIFURCATION CURVES; PERIODIC WINDOWS; TWO-PARAMETER MAPS;

NONLINEAR ANALYSIS;

EID: 45049083940     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2007.11.014     Document Type: Article

References (25)

1. Benedicks M., and Carleson L. The dynamics of the Hénon map. Ann. Math. 133 (1991) 73-169
2. Carcassès J.P., Mira C., Bosch M., Simó C., and Tatjer J.C. Crossroad area-spring area transition. (1) Parameter plane representation. Internat J. Bifur. Chaos 1 (1991) 183-196
3. Collet P., and Eckmann J.-P. On the abundance of aperiodic behavior for maps of the interval. Commun. Math. Phys. 73 (1980) 115-160
4. Curry J.H. On the Hénon transformation. Comm. Math. Phys. 68 (1979) 129-140
5. Feigenbaum M. Quantitative universality for a class of nonlinear transformations. J. Stat. Phys. 19 (1978) 25-52
6. Feit S.B. Characteristic exponents and strange attractors. Comm. Math. Phys. 61 (1978) 249-260
7. Guckenheimber J., and Holmes P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (1983), Springer, New York
8. Hénon M. A two-dimensional mapping with a strange attractor. Commun. Math. Phys. 50 (1976) 69-77
9. Hitzl D.L., and Zele F. An exploration of the Hénon map. Physica D 14 (1985) 305-326
10. Hunt B.H., Kennedy J.A., Li T.-Y., and Nusse H.E. SLYRB measures: natural invariant measures for chaotic systems. Physica D 170 (2002) 50-71
11. Jakobson M.V. Absolutely continuous measures for one-parameter families of one-dimensional maps. Comm. Math. Phys. 81 (1981) 39-88
12. Julia G. Mémoire sur l'itération des fonctions rationelles. J. Math. Pure Appl. 4 (1918) 47-245
13. Lauwerier H.A. In: Holden C., and A.V. (Ed). One-dimensional Iterative Maps (1986), Princeton Univ. Press, Princeton
14. Lorenz E.N. The problem of deducing the climate from the governing equations. Tellus 16 (1964) 1-11
15. Lozi R. Un attracteur étrange (?) due type attracteur de Hénon. J. Phys. (Paris) 39 (1978) 9-10
16. May R.M. Simple mathematical models with very complicated dynamics. Nature 261 (1976) 459-467
17. Mira C. Chaotic Dynamics. From the One-Dimensional Endomorphism to the Two-dimensional Diffeomorphism (1987), World Scientific, Singapore
18. Mira C., Carcassès J.P., Bosch M., Simó C., and Tatjer J.C. Crossroad area-spring area transition. (2) Foliated parameter representation. Internat J. Bifur. Chaos 1 (1991) 339-348
19. Mira C., and Carcassès J.P. On the "crossroad area-saddle area" and "crossroad area-spring area" transitions. Internat. J. Bifur. Chaos 1 (1991) 641-655
20. Olsen L.F., and Degn H. Chaos in biological systems. Q. Rev. Biophys. 18 (1985) 165-225
21. Simó C. On the Hénon-Pomeau attractor. J. Stat. Phys. 21 (1979) 465-494
22. Gallas J.A.C. Structure of the parameter space of the Hénon map. Phys. Rev. Let. 70 (1993) 2714
23. Gallas J.A.C. Dissecting shrimps: results for some one-dimensional physical systems. Physica A 202 (1994) 196
24. Bonatto C., Gallas J.A.C., and Ueda Y. Chaotic phase similarities and recurrences in a damped-driven Duffling oscillator. Phys. Rev. E 77 (2008) 026217
25. Hunt B.R.., Gallas J.A.C., Grebogi C., Yorke J.A., and Koçak H. Bifurcation rigidity. Physica D 129 (1999) 35