The Behavior of Transformations on Intervals and Manifolds

  • Andrzej Lasota
  • Michael C. Mackey
Part of the Applied Mathematical Sciences book series (AMS, volume 97)


This chapter is devoted to a series of examples of transformations on intervals and manifolds whose asymptotic behavior can be explored through the use of the material developed in Chapter 5 Although results are often stated in terms of the asymptotic stability of {P n }, where P is a Frobenius—Perron operator corresponding to a transformation S, remember that, according to Proposition 5.6.2, S is exact when {P n } is asymptotically stable and S is measure preserving.


Asymptotic Stability Tangent Vector Stationary Density Bounded Variation Induction Argument 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Andrzej Lasota
    • 1
  • Michael C. Mackey
    • 2
  1. 1.Institute of MathematicsSilesian UniversityKatowicePoland
  2. 2.Center of Nonlinear DynamicsMcGill UniversityMontrealCanada

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