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For almost every tent map, the turning point is typical

Henk Bruin (1998)

Fundamenta Mathematicae

Let T a be the tent map with slope a. Let c be its turning point, and μ a the absolutely continuous invariant probability measure. For an arbitrary, bounded, almost everywhere continuous function g, it is shown that for almost every a, ʃ g d μ a = l i m n 1 n i = 0 n - 1 g ( T a i ( c ) ) . As a corollary, we deduce that the critical point of a quadratic map is generically not typical for its absolutely continuous invariant probability measure, if it exists.

Foreword

(1979)

Abstracta. 7th Winter School on Abstract Analysis

Fourier-Feynman transforms of unbounded functionals on abstract Wiener space

Byoung Kim, Il Yoo, Dong Cho (2010)

Open Mathematics

Huffman, Park and Skoug established several results involving Fourier-Feynman transform and convolution for functionals in a Banach algebra S on the classical Wiener space. Chang, Kim and Yoo extended these results to abstract Wiener space for a more generalized Fresnel class 𝒜 1 , 𝒜 2 A1,A2 than the Fresnel class (B)which corresponds to the Banach algebra S. In this paper we study Fourier-Feynman transform, convolution and first variation of unbounded functionals on abstract Wiener space having the form...

Fractal negations.

Gaspar Mayor Forteza, Tomasa Calvo Sánchez (1994)

Mathware and Soft Computing

From the concept of attractor of a family of contractive affine transformations in the Euclidean plane R2, we study the fractality property of the De Rham function and other singular functions wich derive from it. In particular, we show as fractals the strong negations called k-negations.

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