Tricornとattracting odd order cyclesの分岐
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概要
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A family of antiholomorphic maps : fc(z)=z^-2+c(c∈C) is considered. The connectedness locus for this family is called "tricorn" or "Mandelbar set". Computer experiment suggests that attracting odd order cycles for this family bifurcate along piecewise smooth curves with three cusps, which are called "deltoids". This phenomenon never appears for analytic families of polynomials. In this note, a sufficient condition for saddle-node bifurcation of such cycles along deltoids is given. This condition seems to be necessary.
- 東京工芸大学の論文
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