Download Bifurcation and Chaos: Theory and Applications by Professor Jan Awrejcewicz (auth.), Professor Jan Awrejcewicz PDF

By Professor Jan Awrejcewicz (auth.), Professor Jan Awrejcewicz (eds.)

Bifurcation and Chaos provides a set of specifically written articles describing the idea and alertness of nonlinear dynamics to a wide selection of difficulties encountered in physics and engineering. every one bankruptcy is self-contained and contains an easy creation, an exposition of the current state-of-the-art, and info of contemporary theoretical, computational and experimental effects. integrated one of the functional platforms analysed are: hysteretic circuits, Josephson circuits, magnetic platforms, railway dynamics, rotor dynamics and nonlinear dynamics of speech. This e-book comprises very important details and concepts for all mathematicians, physicists and engineers whose paintings in R&D or academia comprises the sensible end result of chaotic dynamics.

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18. 1; b) function g( A), preserving the phase transition only g(A) undergoes a phase transition (see Fig. 18 a, b). The other specific scaling functions remain unaffected. As can be easily imagined, a different choice of the properties of the added hyperbolic element can provoke other combinations of phase transitions. 44 R. Stoop 5. Conclusions Using the generalized thermodynamic formalism, a more refined description of the properties of dynamical systems has been given. With the help of appropriate models, the theoretical tools were outlined which permit one to predict and understand the problems which arise for the numerical characterization of the scaling behavior in dissipative dynamical systems.

Then individual "partial" free energy functions, entropies, Lyapunov exponents and dimensions are calculated separately for each direction [14]. This procedure, however, applies only to hyperbolic maps. For example, nonhyperbolic maps can show the well-known effect of homoclinic tangencies. At those points, it is not possible to factorize into a contracting and an expanding direction. Usually it is hoped that the factorization procedure can be followed also for nonhyperbolic maps, with the exception of a set of points of small measure.

Theor. Phys. 63, 1804 (1980) 18. B. Mandelbrot: The fractal geometry of nature. Freeman, New York 1982 19. J. Peinke, J. Parisi, R. E. Roessler: An encounter with chaos. Springer, in press (1992) 20. L. Devaney: An introduction to chaotic dynamical systems. Benjamin, Menlo Park CAL 1986 On the Complete Characterization of Chaotic Attractors 45 21. N. Shtern: The dimension of turbulent motion attractors. Dokl. Akad. Nauk. SSSR 270, 582 (1983) 22. F. Hausdorff: Math. Ann. 79, 157 (1919) 23. A. Renyi: Probability theory.

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