Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms |
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Authors: | J Palis F Takens |
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Institution: | (1) IMPA, Estr. Dona Castorina 110, Horto, Rio de Janeiro, Brazil;(2) Mathematisch Instituut, Rijksuniversiteit Groningen, Postbus 800, NL-Groningen, The Netherlands |
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Abstract: | Summary We describe a large class of one-parameter families , {}, , of two-dimensional diffeomorphisms which arestable for <0, exhibit acycle for =0, and thereafter have a bifurcation set of positive but arbitrarily smallrelative measure for in small intervals 0, ]. A main assumption is that the basic sets involved in the cycle havelimit capacities that are not too large.The second author acknowledges hospitality and financial support from IMPA/CNPq during the period this paper was prepared |
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