The First Bifurcation & the First Tangency inside the Horseshoe (第2&3回複雑系札幌シンポジウム講究録) THE FIRST BIFURCATION & THE FIRST TANGENCY INSIDE THE HORSESHOE :
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We introduce a general definition of first homoclinic tangency, and construct a 1-parameter family of planar diffeomorphisms from Smale's n-fold horseshoe diffeomorphism, which has the first homoclinic tangency that is a first bifurcation introduced by Palis and Takens. Moreover, the limit capacity of its maximal invariant set associated with this first bifurcation can be as small as is required.
物性研究 66(4), 807-814, 1996-07