Inventiones mathematicae

, Volume 82, Issue 3, pp 397–422 | Cite as

Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms

  • J. Palis
  • F. Takens


We describe a large class of one-parameter families φ, {ϕμ}, μ∈ℝ, of two-dimensional diffeomorphisms which arestable for μ<0, exhibit acycle for μ=0, and thereafter have a bifurcation set of positive but arbitrarily smallrelative measure for μ in small intervals [0, σ]. A main assumption is that the basic sets involved in the cycle havelimit capacities that are not too large.


Large Class Small Interval Main Assumption 
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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • J. Palis
    • 1
  • F. Takens
    • 2
  1. 1.IMPARio de JaneiroBrazil
  2. 2.Mathematisch InstituutRijksuniversiteit GroningenNL-GroningenThe Netherlands

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