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Basic sets: Sets that determine the dimension of basin boundaries. (English) Zbl 0674.58031
Dynamical systems, Proc. Spec. Year, College Park/Maryland, Lect. Notes Math. 1342, 220-250 (1988).
[For the entire collection see Zbl 0653.00011.]
The authors note that the boundary of a basin of attraction of an attractor can have different dimensions in different regions, if this boundary is fractal. They conjecture that the number of possible dimensions is at most the number of some well defined asymptotic sets (called basic sets) on the basin boundary and prove the conjecture for Axiom A two dimensional diffeomorphisms and one dimensional chaotic maps. In addition a numerical treatment of an example is given.
Reviewer: N.Ivanov

37D99 Dynamical systems with hyperbolic behavior