Discontinuity of Hausdorff dimension and limit capacity on arcs of diffeomorphisms

Abstract

We consider one-parameter families of torus diffeomorphisms that bifurcate from global hyperbolic maps (Anosov) to DA maps (derived from Anosov). For an open set of these families, we show that the Hausdorff dimension and limit capacity of the nonwandering set are not continuous across the bifurcation. We also study the behaviour of equilibrium measures near the bifurcation. © 1989, Cambridge University Press. All rights reserved.