Hausdorff dimension of attractors for two dimensional Lorenz transformations
The author considers the two-dimensional Lorenz transformation \[ F(x, y) = (T(x), g(x,y)), \] where \(T\) is a piecewise monotonic topologically transitive and expanding transformation on \([0, 1],\) \(g(x, y): [0, 1]^2 \to [0, 1]\) is piecewise differentiable. It is proved that the Hausdorff dimension of the attractor of \(F\) equals \(z+1\) where \(z\) is the unique zero of the pressure function \(t \to p(F, t\varphi)\), \(\varphi = \log |\partial g / \partial y|\).
scientific article; zbMATH DE number 1445783
scientific article