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The ƒ(a) formalism applied to the crossover from conservative to dissipative scaling behaviour in period doubling systems

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

Abstract

We use the ƒ(a) (spectral dimension) formalism to give a global description of the crossover from conservative to dissipative scaling behaviour in period doubling systems. As a generic model we consider the two-dimensional Hénon map, for which the jacobian 0 ⩽ B ⩽ 1 measures the amount of dissipation, and we calculate the successive approximants ƒk(a, B) to the generalized spectral dimension for small (i.e. experimentally feasible) values of k. The crossover properties from the extreme dissipative case (B = 0) to the conservative case (B = 1) are discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:147:y:1987:i:1:p:297-314
    DOI: 10.1016/0378-4371(87)90112-9
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    References listed on IDEAS

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    1. 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.
    2. Feigenbaum, Susan & Ortiz, Henry & Willett, Thomas D, 1985. "Protectionist Pressures and Aggregate Economic Conditions: Comment [Pressures for Protectionism: An Empirical Analysis]," Economic Inquiry, Western Economic Association International, vol. 23(1), pages 175-182, January.
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