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Paper   IPM / Physic / 6849
School of Physics
  Title:   Hierarchy of Chaotic Maps with An Invariant Measure and Their Coupling
  Author(s): 
1.  M.A. Jafarizadeh
2.  S. Behnia
  Status:   Published
  Journal: Physica D: Nonlinear Phenomena
  No.:  111
  Vol.:  159
  Year:  2001
  Pages:   1-21
  Supported by:  IPM
  Abstract:
Hierarchy of one-parameter families of chaotic maps with an invariant measure have been introduced, where their appropriate coupling has led to the generation of some coupled chaotic maps with an invariant measure. It is shown that these chaotic maps (also the coupled maps) do not undergo any period doubling or period-n-tupling cascade bifurcation to chaos, but they have either single fixed point attractor at certain values of the parameters or they are ergodic in the complementary region. Using the invariant measure or SinaiRuelleBowen measure the KolmogrovSinai entropy of the chaotic maps (coupled maps) have been calculated analytically, where the numerical simulations support the results.

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