Wyniki wyszukiwania

1

An arithmetic group associated with a Pisot unit, and its symbolic-dynamical representation

100%

Sidorov N.

Acta Arithmetica

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2002

|

tom 101

|

nr 3

199-213

2

Multidimensional self-affine sets: non-empty interior and the set of uniqueness

63%

Hare K., Sidorov N.

Studia Mathematica

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2015

|

tom 229

|

nr 3

223-232

EN

Let M be a d × d real contracting matrix. We consider the self-affine iterated function system {Mv-u, Mv+u}, where u is a cyclic vector. Our main result is as follows: if $|det M| ≥ 2^{-1/d}$, then the attractor $A_{M}$ has non-empty interior. We also consider the set $𝒰_{M}$ of points in $A_{M}$ which have a unique address. We show that unless M belongs to a very special (non-generic) class, the Hausdorff dimension of $𝒰_{M}$ is positive. For this special class the full description of $𝒰_{M}$ is given as well. This paper continues our work begun in two previous papers.

3

On the topology of sums in powers of an algebraic number

63%

Sidorov N., Solomyak B.

Acta Arithmetica

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2011

|

tom 149

|

nr 4

337-346

4

Number of representations related to a linear recurrent basis

51%

Dumont J., Sidorov N., Thomas A.

Acta Arithmetica

|

1999

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tom 88

|

nr 4

371-396

Ograniczanie wyników

3 Acta Arithmetica

1 Studia Mathematica

4 Sidorov N.

1 Dumont J.

1 Hare K.

1 Solomyak B.

1 Thomas A.

1 2015

1 2011

1 2002

1 1999

An arithmetic group associated with a Pisot unit, and its symbolic-dynamical representation

Multidimensional self-affine sets: non-empty interior and the set of uniqueness

On the topology of sums in powers of an algebraic number

Number of representations related to a linear recurrent basis