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Period doubling in maps with a maximum of order z

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  • Van Der Weele, J.P.
  • Capel, H.W.
  • Kluiving, R.

Abstract

We consider the scaling behaviour in period-doubling systems, exemplified by the one-dimensional map χn+1 = 1 − λ|χn|z, which has a maximum of order z (z > 1). The Feigenbaum scaling factors α and δ are studied as functions of z, and more generally the scaling functions 1/σ and ƒ(a). In particular, using the universal functions g(x) and h(x) we establish the inequality δ < αz, which implies that δ remains finite (≲ 30) in the limit z → ∞.

Suggested Citation

  • Van Der Weele, J.P. & Capel, H.W. & Kluiving, R., 1987. "Period doubling in maps with a maximum of order z," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 145(3), pages 425-460.
    • Handle: RePEc:eee:phsmap:v:145:y:1987:i:3:p:425-460
    DOI: 10.1016/0378-4371(87)90004-5
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    1. Skogan, Wesley G., 1982. "Police and Community in Japan. By Walter L. Ames. (Berkeley: University of California Press, 1981. Pp. xvi + 245. $22.50.)," American Political Science Review, Cambridge University Press, vol. 76(3), pages 679-680, September.
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    1. Van Der Weele, J.P. & Capel, H.W., 1987. "The ƒ(a) formalism applied to the crossover from conservative to dissipative scaling behaviour in period doubling systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 147(1), pages 297-314.
    2. Post, T. & Capel, H.W. & Van der Weele, J.P., 1989. "Phase-length distributions in intermittent band switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 160(3), pages 321-350.
    3. Post, Thijs & Capel, Hans W., 1991. "Windows in one-dimensional maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(1), pages 62-100.

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    1. Post, Thijs & Capel, Hans W., 1991. "Windows in one-dimensional maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 178(1), pages 62-100.

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