Journal of Statistical Physics

, Volume 121, Issue 5–6, pp 759–778 | Cite as

Weak Noise Approach to the Logistic Map

  • Hans C. FogedbyEmail author
  • Mogens H. Jensen


Using a nonperturbative weak noise approach we investigate the interference of noise and chaos in simple 1D maps. We replace the noise-driven 1D map by an area-preserving 2D map modelling the Poincare sections of a conserved dynamical system with unbounded energy manifolds. We analyze the properties of the 2D map and draw conclusions concerning the interference of noise on the nonlinear time evolution. We apply this technique to the standard period-doubling sequence in the logistic map. From the 2D area-preserving analogue we, in addition to the usual period-doubling sequence, obtain a series of period doubled cycles which are elliptic in nature. These cycles are spinning off the real axis at parameters values corresponding to the standard period doubling events.


Weak noise random maps Hamiltonian systems elliptic fixed points period doubling 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Physics and AstronomyUniversity of AarhusAarhus CDenmark
  2. 2.NORDITACopenhagen ØDenmark
  3. 3.Niels Bohr Institute for Astronomy, Physics, and GeophysicsCopenhagen ØDenmark

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