On the continuity of Hausdorff dimension and limit capacity for horseshoes

1988 ◽  
pp. 150-160 ◽  
Author(s):  
J. Palis ◽  
M. Viana
Keyword(s):  
Hausdorff Dimension ◽  
Limit Capacity

scholarly journals Discontinuity of Hausdorff dimension and limit capacity on arcs of diffeomorphisms

1989 ◽  
Vol 9 (3) ◽  
pp. 403-425 ◽  
Author(s):  
Lorenzo J. Diaz ◽  
Marcelo Viana
Keyword(s):  
Hausdorff Dimension ◽  
Equilibrium Measures ◽  
Open Set ◽  
Limit Capacity ◽  
Nonwandering Set

AbstractWe 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.

Fractal dimension: Limit capacity or Hausdorff dimension?

1990 ◽  
Vol 58 (10) ◽  
pp. 986-988 ◽  
Author(s):  
Christopher Essex ◽  
M. A. H. Nerenberg
Keyword(s):  
Fractal Dimension ◽  
Hausdorff Dimension ◽  
Limit Capacity

scholarly journals Minimal F2-flows

1985 ◽  
Vol 39 (2) ◽  
pp. 187-193
Author(s):  
Daniel Berend
Keyword(s):  
Hausdorff Dimension ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Affine Transformations ◽  
Dimensional Torus ◽  
Minimal Sets ◽  
Necessary And Sufficient

AbstractLet σ be an ergodic endomorphism of the r–dimensional torus and Π a semigroup generated by two affine transformations lying above σ. We show that the flow defined by Π admits minimal sets of positive Hausdorff dimension and we give necessary and sufficient conditions for this flow to be minimal.

Length distortion and the Hausdorff dimension of limit sets

2000 ◽  
Vol 122 (3) ◽  
pp. 465-482 ◽  
Author(s):  
Martin Bridgeman ◽  
Edward C. Taylor
Keyword(s):  
Hausdorff Dimension ◽  
Limit Sets ◽  
Length Distortion
Sign in / Sign up

Export Citation Format

Share Document