The lakes of Wada are three disjoint simply connected domains in S2 with the counterintuitive property that they all have the same boundary. The common boundary is a indecomposable continuum. In this article we calculated the Minkowski dimension of such boundaries. The lakes constructed in the standard Cantor way has ln(6)/ ln(3) ≈ 1.6309-dimensional boundary, while in general, for any number in [1, 2] we can construct lakes with such dimensional boundaries.

Let H: C^2 -> C^2 be the Henon mapping given by (x,y) --> (p(x) - ay,x). The key invariant subsets are K_+/-, the sets of points with bounded forward images, J_+/- = the boundary of K_+/-, J = the… Expand

Fractals in probability and analysis, Cambridge Studies in Advanced Mathematics, 162

2017

Oberste-Vorth, R.W.: Hénon mappings in the complex domain. II. Projective and inductive limits of polynomials, Real and complex dynamical systems (Hillerød