The term ‘chaos’ is used in reference to unstable, aperiodic motion in dynamical systems and also to the state of a system which exhibits such motion. Almost any nonequilibrium open system will, when some bifurcation parameter characterizing the system is made sufficiently large, display chaotic behavior. It can be said that chaos is Nature’s universal dynamical form. Chaos is characterized by the coexistence of an infinite number of unstable periodic orbits that determine the form and structure of the chaotic behavior exhibited by any given system. In this chapter we consider the problem of identifying the descriptive signature of such a set of orbits, and we establish the point of view from which we will elucidate the nature of chaos.
KeywordsPeriodic Orbit Invariant Manifold Unstable Manifold Chaotic Attractor Fluid Particle
Unable to display preview. Download preview PDF.
- Baker, G.L., Gollub, J.P. (1990) Chaotic Dynamics, An Introduction. Cambridge University Press, New YorkGoogle Scholar
- Berge, P., Pomeau, Y., Vidal, C. (1984) Order Within Chaos. Hermann, Paris Eckmann, J.-P., Ruelle, D. (1985) Ergodic theory of chaos and strange attractors. Rev. Mod. Phys. 57, 617–656Google Scholar
- Guckenheimer, J., Holmes, P. (1986) Nonlinear Oscillations, Dynamical Systems, and Bifurcations and Vector Fields, 2nd edn. Springer, Berlin, HeidelbergGoogle Scholar
- Ottino, J.M. (1989) The kinematics of mixing: stretching, chaos and trans¬port. Cambridge University Press, New YorkGoogle Scholar
- Rasband, S.N. (1990) Chaotic Dynamics of Nonlinear Systems. Wiley, New YorkGoogle Scholar
- Sinai, Y.G. (1981) Randomness in non-random systems. Nature No. 3, 72–80Google Scholar
- Takahashi, Y.,(1980) Chaos, periodic points and entropy. Butsuri 35,149–161 (Japanese)Google Scholar
- Wiggins, S. (1992) Chaotic transport in dynamical systems. Springer, Berlin, HeidelbergGoogle Scholar