Abstract
In the development of science in the twentieth century, philosophers and scientists convinced that there could be a motion even for a simple system which is erratic in nature, not simply periodic or quasiperiodic. Moreover, the behaviors of the motion may be unpredictable and therefore long-range prediction is impossible. The science of unpredictability has immense interest.
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References
Simmons, G.F.: Introduction to Topology and Modern Analysis. Tata McGraw-Hill (2004)
Munkres, J.R.: Topology. Prentice Hall (2000)
Copson, E.T.: Metric Spaces. Cambridge University Press (1968)
Reisel, R.B.: Elementary Theory of Metric Spaces. Springer-Verlag (1982)
Bahi, J.M., Guyeux, C.: Discrete Dynamical Systems and Chaotic Mechanics: Theory and Applications. CRC Press (2013)
Ott, E.: Chaos in Dynamical Systems, 2nd edition. Cambridge University press (2002)
Yorke, J.A., Grebogi, C., Ott, E., Tedeschini-Lalli, L.: Scaling behavior of windows in dissipative dynamical systems. Phys. Rev. Lett. 54, 1095–1098 (1985)
Grebogi, C., Ott, E., Yorke, J.A.: Chaos, Strange attractors, and fractal basin boundaries in nonlinear dynamics. Science 238, 632–638 (1987)
Devaney, R.L.: An Introduction to Chaotic Dynamical systems. Westview Press (2003)
Metropolis, N., Stein, M.L., Stein, P.R.: On finite limit sets for transformations on the unit interval. J. Comb. Theory (A) 15, 25–44 (1973)
Feigenbaum, M.J.: The universal metric properties of nonlinear transformations. J. Stat. Phys. 21, 669–706 (1979)
Royden, H.L.: Real Analysis. Pearson Education (1988)
Li, T., Yorke, J.A.: Period three implies chaos. Am. Math. Monthly 82, 985–992 (1975)
Glendinning, P.: Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations. Cambridge University Press (1994)
Gluckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer (1983)
Jordan, D.W., Smith, P.: Non-linear Ordinary Differential Equations. Oxford University Press (2007)
McCauley, J.L.: Chaos, Dynamics and Fractals. Cambridge University Press (1993)
Smale, S.: Differentiable dynamical systems. Bull. Am. Math. Soc. 73, 747–817 (1967)
Pomeau, Y., Manneville, P.: Intermittent transition to turbulence in dissipative dynamical systems. Commun. Math. Phys. 74, 189 (1980)
Benettin, G., Cercignani, C., Galgani, L., Giorgilli, A.: Universal properties in conservative dynamical systems. Lett. Nuovo Cimento 28, 1–4 (1980)
Gleick, J.: Chaos: Making a new science. Viking, New York (1987)
Devaney, R.L.: A First Course in Chaotic Dynamical Systems: Theory and Experiment. Westview Press (1992)
Davies, B.: Exploring Chaos. Westview Press (2004)
Cvitanović, P.: Universality in Chaos, 2nd edn. IOP, Bristol and Philadelphia (1989)
Arrowsmith, D.K., Place, L.M.: Dynamical Systems: Differential Equations, Maps and Chaotic Behavior. Chapman and Hall/CRC (1992)
Addison, P.S.: Fractals and Chaos: An Illustrated Course. Overseas Press (2005)
Manneville, P.: Instabilities, An introduction to Nonlinear Dynamics and Complex Systems. Imperial College Press, Chaos and Turbulence (2004)
Lorenz, E.: The Essence of Chaos. University of Washington Press (1993)
Tél, T., Gruiz, M.: Chaotic Dynamics: An Introduction Based on Classical Mechanics. Cambridge University Press (2006)
Sternberg, S.: Dynamical Systems. Dover Publications (2010)
Parker, T.S., Chua, L.O.: Practical Numerical Algorithms for Chaotic Systems. Springer-Verlag New York Inc. (1989)
Stewart, I.: Does God play dice?: The Mathematics of Chaos. Oxford (1990)
Gulick, D.: Encounters with Chaos and Fractals. CRC Press (2012)
Bhi-lin, H.: Elementary Symbolic Dynamics and Chaos in Dissipative Systems. World Scientific (1989)
Baker, G.L., Gollub, J.P.: Chaotic Dynamics: An Introduction. Cambridge University Press (1990)
McMullen, C.T.: Complex Dynamics and Renormalization. Princeton University Press (1994)
Medio, A., Lines, M.: Nonlinear Dynamics: A Primer. Cambridge University Press (2001)
Feigenbaum, M.J.: Universal behavior in nonlinear systems. Los Alamos Science 1, 4–27 (1980)
Hilborn, R.C.: Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers. Oxford University Press (2000)
Lichtenberg, A.J., Lieberman, M.A.: Regular and Stochastic Motion. Springer, Berlin (1983)
Schuster, H.G.: Deterministic Chaos, Chaps. 1, 2. Physik-Verlag, Weinheim (1984)
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Layek, G.c. (2015). Chaos. In: An Introduction to Dynamical Systems and Chaos. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2556-0_12
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DOI: https://doi.org/10.1007/978-81-322-2556-0_12
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