Displaying similar documents to “Continuity of the Hausdorff dimension for invariant subsets of interval maps.”

On the continuity of the pressure for monotonic mod one transformations

Peter Raith (2000)

Commentationes Mathematicae Universitatis Carolinae

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If f : [ 0 , 1 ] → ℝ is strictly increasing and continuous define T f x = f ( x ) ( mod 1 ) . A transformation T ˜ : [ 0 , 1 ] → [ 0 , 1 ] is called ε -close to T f , if T ˜ x = f ˜ ( x ) ( mod 1 ) for a strictly increasing and continuous function f ˜ : [ 0 , 1 ] → ℝ with ∥ f ˜ - f ∥ ∞ < ε . It is proved that the topological pressure p ( T f , g ) is lower semi-continuous, and an upper bound for the jumps up is given. Furthermore the continuity of the maximal measure is shown, if a certain condition is satisfied. Then it is proved that the topological pressure is upper semi-continuous for every continuous function g : [ 0 , 1 ] → ℝ , if and...