$Complex continued fractions with restricted entries$

Complex continued fractions with restricted entries

We study special infinite iterated function systems derived from complex continued fraction expansions with restricted entries. We focus our attention on the corresponding limit set whose Hausdorff dimension will be denoted by $h$. Our primary goal is to determine whether the $h$-dimensional Hausdor...

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Bibliographic Details
Main Authors:	Pawel Hanus, Mariusz Urbanski
Format:	Article
Language:	English
Published:	Texas State University 1998-10-01
Series:	Electronic Journal of Differential Equations
Subjects:	iterated function systems complex continued fractions Hausdorff dimension Hausdorff measure packing measure.
Online Access:	http://ejde.math.txstate.edu/Volumes/1998/27/abstr.html

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spelling	doaj-f8d02e671480424489ecf46807787f7d2020-11-24T20:55:03ZengTexas State UniversityElectronic Journal of Differential Equations1072-66911998-10-0119982719Complex continued fractions with restricted entriesPawel HanusMariusz UrbanskiWe study special infinite iterated function systems derived from complex continued fraction expansions with restricted entries. We focus our attention on the corresponding limit set whose Hausdorff dimension will be denoted by $h$. Our primary goal is to determine whether the $h$-dimensional Hausdorff and packing measure of the limit set is positive and finite. http://ejde.math.txstate.edu/Volumes/1998/27/abstr.htmliterated function systemscomplex continued fractionsHausdorff dimensionHausdorff measurepacking measure.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Pawel Hanus Mariusz Urbanski
spellingShingle	Pawel Hanus Mariusz Urbanski Complex continued fractions with restricted entries Electronic Journal of Differential Equations iterated function systems complex continued fractions Hausdorff dimension Hausdorff measure packing measure.
author_facet	Pawel Hanus Mariusz Urbanski
author_sort	Pawel Hanus
title	Complex continued fractions with restricted entries
title_short	Complex continued fractions with restricted entries
title_full	Complex continued fractions with restricted entries
title_fullStr	Complex continued fractions with restricted entries
title_full_unstemmed	Complex continued fractions with restricted entries
title_sort	complex continued fractions with restricted entries
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	1998-10-01
description	We study special infinite iterated function systems derived from complex continued fraction expansions with restricted entries. We focus our attention on the corresponding limit set whose Hausdorff dimension will be denoted by $h$. Our primary goal is to determine whether the $h$-dimensional Hausdorff and packing measure of the limit set is positive and finite.
topic	iterated function systems complex continued fractions Hausdorff dimension Hausdorff measure packing measure.
url	http://ejde.math.txstate.edu/Volumes/1998/27/abstr.html
work_keys_str_mv	AT pawelhanus complexcontinuedfractionswithrestrictedentries AT mariuszurbanski complexcontinuedfractionswithrestrictedentries
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Complex continued fractions with restricted entries

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