Connecting period-doubling cascades to chaos

International Journal of Bifurcation and Chaos

Volumn 22, Issue 2, 2012, Pages

  Sander, Evelyn ^a   Yorke, James A ^b,c  

^a GEORGE MASON UNIVERSITY   (United States)

^b IPST   (United States)

^c Bldg 142   (United States)

Author keywords

Bifurcation; cascades; chaos; period doubling

Indexed keywords

BIFURCATION (MATHEMATICS); CASCADES (FLUID MECHANICS);

BIFURCATION DIAGRAM; CHAOTIC BEHAVIORS; DUFFING EQUATIONS; FORCED DAMPED PENDULUMS; PERIOD DOUBLING; PERIOD DOUBLING BIFURCATION; PERIOD DOUBLING CASCADE; PROMINENT FEATURES;

CHAOS THEORY;

EID: 84858735658     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127412500228     Document Type: Review

References (15)

1. Bowen, R. [1970] "Topological entropy and axiom A", Global Analysis, Proc. Symp. Pure Math., Vol. XIV, Berkeley, Calif., 1968 (Amer. Math. Soc, Providence, R. I.), pp. 23-41.
2. Chung, Y. M. [2001] "Topological entropy for differentiable maps of intervals", Osaka J. Math. 38, 1-12.
3. Chung, Y. M. & Hirayama, M. [2003] "Topological entropy and periodic orbits of saddle type for surface diffeomorphisms", Hiroshima Math. J. 33, 189-195.
4. Feigenbaum, M. J. [1979] "The universal metric properties of nonlinear transformations", J. Statist. Phys. 21, 669-706.
5. Joglekar, M. R., Sander, E. & Yorke, J. A. [2010] "Fixed points indices and period-doubling cascades", J. Fixed Point Th. Appl. 8, 151-176.
6. Kan, I., Kocak, H. & Yorke, J. A. [1992] "Antimonotonicity: Concurrent creation and annihilation of periodic orbits", Ann. Math. 136, 219-252.
7. Katok, A. & Mezhirov, A. [1998] "Entropy and growth of expanding periodic orbits for one-dimensional maps", Fund. Math. 157, 245-254, dedicated to the memory of Wieslaw Szlenk.
8. Milnor, J. & Thurston, W. [1988] "On iterated maps of the interval", Dynamical Systems (College Park, MD, 1986-87) (Springer, Berlin), pp. 465-563.
9. Misiurewicz, M. & Szlenk, W. [1980] "Entropy of piecewise monotone mappings", Studia Math. 67, 45-63.
10. Myrberg, P. [1962] "Sur l'itération des polynomes réels quadratiques", J. Math. Pures Appl. 41, 339-351.
11. Nusse, H. E., Ott, E. & Yorke, J. A. [1994] "Bordercollision bifurcations: An explanation for observed bifurcation phenomena", Phys. Rev. E 49, 1073-1076.
12. Robinson, C. [1995] Dynamical Systems (CRC Press, Boca Raton).
13. Sander, E. & Yorke, J. A. [2009] "Period-doubling cascades for large perturbations of Hénon families", J. Fixed Point Th. Appl. 6, 153-163.
14. Sander, E. & Yorke, J. A. [2011] "Period-doubling cascades galore", Erg. Th. Dyn. Syst. 31, 1249-1267.
15. Wang, Q. & Young, L.-S. [2001] "Strange attractors with one direction of instability", Comm. Math. Phys. 218, 1-97.