Subadditive pressure for triangular maps

A. Manning, K. Simon

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We investigate properties of the zero of the subadditive pressure used by Falconer, Barreira and Zhang to estimate the box and Hausdorff dimension of a non-conformal repeller. In the conformal case, and in Falconer's 1-bunched non-conformal case, the contraction rates satisfy bounded distortion and so this zero is insensitive to where on each cylinder the contraction is evaluated. We study some nonlinear two-dimensional examples which do not satisfy bounded distortion but do exhibit the same insensitivity. Here the contraction rate fails to specify ellipses that can be used to cover cylinders.

Original languageEnglish
Article number009
Pages (from-to)133-149
Number of pages17
JournalNonlinearity
Volume20
Issue number1
DOIs
Publication statusPublished - Jan 1 2007

Fingerprint

Triangular Map
contraction
Contraction
Box Dimension
Insensitivity
Zero
ellipses
Hausdorff Dimension
boxes
Cover
sensitivity
estimates
Estimate

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Subadditive pressure for triangular maps. / Manning, A.; Simon, K.

In: Nonlinearity, Vol. 20, No. 1, 009, 01.01.2007, p. 133-149.

Research output: Contribution to journalArticle

Manning, A. ; Simon, K. / Subadditive pressure for triangular maps. In: Nonlinearity. 2007 ; Vol. 20, No. 1. pp. 133-149.
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