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Normal points for generic hyperbolic maps

100%

Pollicott M.

Fundamenta Mathematicae

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2009

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tom 206

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nr 1

271-280

EN

We consider families of hyperbolic maps and describe conditions for a fixed reference point to have its orbit evenly distributed for maps corresponding to generic parameter values.

2

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Distributions at infinity for Riemann surfaces

75%

Pollicott M.

Banach Center Publications

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1989

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tom 23

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nr 1

91-100

3

Sets of nondifferentiability for conjugacies between expanding interval maps

51%

Jordan T., Kesseböhmer M., Pollicott M., Stratmann B.

Fundamenta Mathematicae

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2009

|

tom 206

|

nr 1

161-183

EN

We study differentiability of topological conjugacies between expanding piecewise $C^{1+ϵ}$ interval maps. If these conjugacies are not C¹, then their derivative vanishes Lebesgue almost everywhere. We show that in this case the Hausdorff dimension of the set of points for which the derivative of the conjugacy does not exist lies strictly between zero and one. Moreover, by employing the thermodynamic formalism, we show that this Hausdorff dimension can be determined explicitly in terms of the Lyapunov spectrum. These results then give rise to a "rigidity dichotomy" for the type of conjugacies under consideration.

Ograniczanie wyników

2 Fundamenta Mathematicae

1 Banach Center Publications

3 Pollicott M.

1 Jordan T.

1 Kesseböhmer M.

1 Stratmann B.

2 2009

1 1989

Normal points for generic hyperbolic maps

Distributions at infinity for Riemann surfaces

Sets of nondifferentiability for conjugacies between expanding interval maps