Fractal structures in nonlinear dynamics

作者: Jacobo Aguirre , Ricardo L. Viana , Miguel A. F. Sanjuán

DOI: 10.1103/REVMODPHYS.81.333

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摘要: In addition to the striking beauty inherent in their complex nature, fractals have become a fundamental ingredient of nonlinear dynamics and chaos theory since they were defined in the 1970s. Moreover, fractals have been detected in nature and in most fields of science, with even a certain influence in the arts. Fractal structures appear naturally in dynamical systems, in particular associated with the phase space. The analysis of these structures is especially useful for obtaining information about the future behavior of complex systems …

参考文章(307)
Heinz-Otto Peitgen, Hartmut Jürgens, Dietmar Saupe, Chaos and Fractals Chaos and Fractals. ,(2004) , 10.1007/978-1-4757-4740-9
G. Contopoulos, D. Kaufmann, Types of escapes in a simple Hamiltonian system Astronomy and Astrophysics. ,vol. 253, pp. 379- 388 ,(1992)
Edward Ott, Chaos in Dynamical Systems Cambridge University Press. ,(2002) , 10.1017/CBO9780511803260
G. Contopoulos, Asymptotic curves and escapes in Hamiltonian systems Astronomy and Astrophysics. ,vol. 231, pp. 41- 55 ,(1990)
Tamas Tel, Marton Gruiz, Chaotic Dynamics Cambridge University Press. ,(2006) , 10.1017/CBO9780511803277
Benoît B. Mandelbrot, Michael Frame, Fractals, Graphics, and Mathematics Education ,(2002)
Casimir Kuratowski, Sur les coupures irréductibles du plan Fundamenta Mathematicae. ,vol. 6, pp. 130- 145 ,(1924) , 10.4064/FM-6-1-130-145