Universal scaling behaviour for iterated maps in the complex plane

Author:

Manton N. S.,Nauenberg M.

Publisher

Springer Science and Business Media LLC

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Reference12 articles.

1. Eckmann, J.-P.: Roads to turbulence in dissipative dynamical systems. Rev. Mod. Phys.53, 643?654 (1981); Ott, E.: Strange attractors and chaotic motions of dynamical systems. Rev. Mod. Phys.53, 655?671 (1981); Helleman, R.H.G.: In: Fundamental problems in statistical mechanics, Cohen, E.G.D. (ed.). Amsterdam: North Holland 1980; These are three recent review articles which include references to earlier work

2. Shenker, S.J.: Scaling behaviour in a map of a circle into itself: empirical results. Physica5 D, 405?411 (1982); Ostlund, S., Rand, D., Sethna, J., Siggia, E.: A universal transition from quasiperiodicity to chaos in dissipative systems. Phys. Rev. Lett.49, 132?135 (1982)

3. Kadanoff, L.P.: Scaling for a critical Kolmogorov-Arnold-Moser trajectory. Phys. Rev. Lett.47, 1641?1643 (1981); Shenker, S.J., Kadanoff, L.P.: Critical behaviour of a KAM surface: 1. empirical results. J. Stat. Phys.27, 631?656 (1982); Widom, M., Kadanoff, L.P.: Renormalization group analysis of bifurcations in area-preserving maps. Physica5 D, 287?292 (1982)

4. Ruelle, D., Takens, F.: On the nature of turbulence. Commun. Math. Phys.20, 167?192 (1971); Newhouse, S., Ruelle, D., Takens, F.: Occurence of strange axiom A attractors near quasi periodic flows onT m ,m?3. Commun. Math. Phys.64, 35?40 (1978)

5. Schr�der, E.: �ber iterirte Funktionen. Math. Ann.3, 296?322 (1871); Siegel, C.L.: Iteration of analytic functions. Ann. Math.43, 607?612 (1942); For a modern treatment, see Moser, J.K., Siegel, C.L.: Lectures on celestial mechanics. New York: Springer 1971

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