Wyniki wyszukiwania

1

Ergodic averages and free $ℤ^2$ actions

100%

Buczolich Z.

Fundamenta Mathematicae

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1999

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tom 160

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nr 3

247-254

PL

If the ergodic transformations S, T generate a free $ℤ^2$ action on a finite non-atomic measure space (X,S,µ) then for any $c_1,c_2 ∈ ℝ$ there exists a measurable function f on X for which $({N+1})^{-1} ∑_{j=0}^Nf(S^jx) → c_1$ and $(N+1)^{-1} ∑_{j=0}^Nf(T^jx) → c_2 µ$-almost everywhere as N → ∞. In the special case when S, T are rationally independent rotations of the circle this result answers a question of M. Laczkovich.

2

Trajectory of the turning point is dense for a co-σ-porous set of tent maps

63%

Brucks K., Buczolich Z.

Fundamenta Mathematicae

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2000

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tom 165

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nr 2

95-123

EN

It is known that for almost every (with respect to Lebesgue measure) a ∈ [√2,2] the forward trajectory of the turning point of the tent map $T_a$ with slope a is dense in the interval of transitivity of $T_a$. We prove that the complement of this set of parameters of full measure is σ-porous.

3

Lipschitz differences and Lipschitz functions

51%

Balcerzak M., Buczolich Z., Laczkovich M.

Colloquium Mathematicum

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1997

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tom 72

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nr 2

319-324

Ograniczanie wyników

2 Fundamenta Mathematicae

1 Colloquium Mathematicum

3 Buczolich Z.

1 Balcerzak M.

1 Brucks K.

1 Laczkovich M.

1 2000

1 1999

1 1997

Ergodic averages and free $ℤ^2$ actions

Trajectory of the turning point is dense for a co-σ-porous set of tent maps

Lipschitz differences and Lipschitz functions