On scaling properties of two-dimensional maps near the accumulation point of the period-tripling cascade

Regular and Chaotic Dynamics

Volumn 5, Issue 4, 2000, Pages 459-476

  Isaeva, O B ^a   Kuznetsov, S P ^a  

^a INSTITUTE OF RADIO ENGINEERING AND ELECTRONICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2542441916     PISSN: 15603547     EISSN: 14684845     Source Type: Journal    
DOI: 10.1070/RD2000v005n04ABEH000159     Document Type: Review

References (26)

1. H.-O. Peitgen, P. H. Richter. The Beauty of Fractals. Images of Complex Dynamical Systems. Springer-Verlag, 1986.
2. R. L. Devaney. An Introduction to Chaotic Dynamical Systems. Addison-Wesley Publ, 1989.
3. K. M. Briggs, G. R. W. Quispel, C. J. Tomphson. Feigenvalues for Mandelsets. J. Phys. A24, No 14, 1991, P. 3363-3368.
4. J. Milnor. Self-Similarity and Hairiness in the Mandelbrot Set. Computers in Geometry and Topology, 114, 1989, P. 211-257.
5. P. Cvitanović, J. Myrheim. Complex Universality. Commun. Math. Phys., 121, No 2, 1989, P. 225-254.
6. M. J. Feigenbaum. Quantitative Universality for a Class of Non-Linear Transformations. J. Stat. Phys., 19, No 1, 1978, P. 25-52.
7. M. J. Feigenbaum. The Universal Metric Properties of Non-Linear Transformations. J. Stat. Phys., 21, No 6, 1979, P. 669-706.
8. M. Feigenbaum. Universality in Behavior of Nonlinear Systems. Usp. Fiz. Nauk, V. 141, No 2, 1983, P. 343-374.
9. E. B. Vul, Y. G. Sinai, K. M. Khanin. Feigenbaum Universality and the Thermodynamic Formalism. Russ. Math. Surv., 39, No 3, 1984, P. 1-40.
10. M. Nauenberg. Fractal Boundary of Domain of Analyticity of the Feigenbaum Function and Relation to the Mandelbrot Set. J. Stat. Phys., V. 47, No 3-4, 1987, P. 459-475.
11. A. L. J. Wells, R. E. Overill. The Extension of the Feigenbaum- Cvitanović Function to the Complex Plane. Int. J. of Bifurcation and Chaos. V. 4, No 4, 1994, P. 1041-1051.
12. A. I. Golberg, Y. G. Sinai, K. M. Khanin. Universal Properties for Sequences of Bifurcations of Period 3. Russ. Math. Surv., V. 38, No 1, 1983, P. 187-188.
13. P. Cvitanović, J. Myrheim. Universality for Period n-Tuplings in Complex Mappings. Phys. Lett. A94, No 8, 1983, P. 329-333.
14. C. Beck. Physical Meaning for Mandelbrot and Julia Set. Physica D125, 1999, P. 171-182.
15. G. H. Gunaratne. Trajectory Scaling for Period Tripling in Near Conformal Mappings. Phys. Rev. A36, 1987, P. 1834-1839.
16. J. Peinke, J. Parisi, B. Rohricht, O. E. Rossler. Instability of the Mandelbrot Set. Zeitsch. Naturforsch. A42, No 3, 1987. P. 263-266.
17. M. Klein. Mandelbrot Set in a Non-Analytic Map. Zeitsch. Naturforsch. A43, No 8-9, 1988, P. 819-820.
18. B. B. Peckham. Real Perturbation of Complex Analytic Families: Points to Regions. Int. J. of Bifurcation and Chaos, V. 8, No 1, 1998, P. 73-93.
19. B. B. Peckham, J. Montaldi. Real Continuation from the Complex Quadratic Family: Fixed-Point Bifurcation Sets. Int. J. of Bifurcation and Chaos, V. 10, No 2, 2000, P. 391-414.
20. J. Argyris, I. Andreadis, T. E. Karakasidis. On Perturbations of the Maldelbrot Map. Chaos, Solitons & Fractals, V. 11, No 7, 2000, P. 1131-1136.
21. J. Rössler, M. Kiwi, B. Hess, M. Marcus. On Perturbations Modulated Non-Linear Processes and a Novel Mechanism to Induce Chaos. Phys. Rev. A39, No 11, 1989, P. 5954-5960.
22. M. Marcus, B. Hess. Lyapunov Exponents of the Logistic Map with Periodic Forcing. Computers & Graphics, V. 13, No 4, 1989, P. 553-558.
23. J. C. Bastos de Figueiredo, C. P. Malta. Lyapunov Graph for Two-Parameters Map: Application to the Circle Map. Int. J. of Bifurcation and Chaos, V. 8, No 2, 1998, P. 281-293.
24. A. P. Kuznetsov, S. P. Kuznetsov, I. R. Sataev. Three-Parameter Scaling for One-Dimensional Maps. Phys. Lett. A189, No 5, 1994, P. 367-373.
25. A. P. Kuznetsov, S. P. Kuznetsov, I. R. Sataev. A Variety of the Period-Doubling Universality Classes in Multi-Parameter Analysis of Transition to Chaos. Physica D109, No 1-2, 1997, P. 91-112.
26. S. P. Kuznetsov, E. Neumann, A. Pikovsky, I. R. Sataev. Critical Point of Tori Collision in Quasiperiodically Forced Systems. Phys. Rev. E62, No 2, 2000, P. 1995-2007.