Hausdorff distance of univoque sets

Authors: Cai, Yi, Komornik, Vilmos

Source: Topology and its Applications. 368:109378

Subject Terms: Mathematics - Number Theory, FOS: Mathematics, Metric theory of other algorithms and expansions, measure and Hausdorff dimension, Number Theory (math.NT), unique \(\beta\)-expansion, 0101 mathematics, Special maps on metric spaces, non-integer base expansions, Radix representation, digital problems, Hausdorff metric, 01 natural sciences

File Description: application/xml

Access URL: http://arxiv.org/abs/2006.16130
https://zbmath.org/8037421
https://doi.org/10.1016/j.topol.2025.109378

Metrical properties of Hurwitz continued fractions

Authors: Bugeaud, Yann, González Robert, Gerardo, Hussain, Mumtaz

Source: Advances in Mathematics. 468:110208

Subject Terms: Relations between ergodic theory and number theory, Approximation by numbers from a fixed field, Hurwitz continued fraction, Continued fractions and generalizations, Mathematics - Number Theory, Mathematics - Complex Variables, Metric theory of other algorithms and expansions, measure and Hausdorff dimension, Hausdorff dimension, Metric Geometry (math.MG), Dynamical Systems (math.DS), Metric theory of continued fractions, Fractals, Hausdorff and packing measures, metric number theory, Mathematics - Metric Geometry, Metric theory, FOS: Mathematics, Number Theory (math.NT), Mathematics - Dynamical Systems, Complex Variables (math.CV)

File Description: application/xml

Access URL: http://arxiv.org/abs/2306.08254
https://zbmath.org/8025827
https://doi.org/10.1016/j.aim.2025.110208

Exceptional sets to Shallit's law of leap years in Pierce expansions

Authors: Min Woong Ahn

Source: Journal of Mathematical Analysis and Applications. 545:129124

Subject Terms: Fractals, leap year, Mathematics - Number Theory, FOS: Mathematics, Metric theory of other algorithms and expansions, measure and Hausdorff dimension, Hausdorff dimension, Primary 11K55, Secondary 28A80, 85A99, Number Theory (math.NT), exceptional set, Pierce expansion

File Description: application/xml

Access URL: http://arxiv.org/abs/2404.18855
https://zbmath.org/7975126
https://doi.org/10.1016/j.jmaa.2024.129124

Hausdorff dimension of singular vectors in function fields

Authors: Aranov, Noy Soffer, Kim, Taehyeong

Source: Advances in Mathematics

Subject Terms: singular vectors, Simultaneous homogeneous approximation, linear forms, Mathematics - Number Theory, lattice point counting, FOS: Mathematics, Metric theory of other algorithms and expansions, measure and Hausdorff dimension, Hausdorff dimension, Number Theory (math.NT), Dynamical Systems (math.DS), Mathematics - Dynamical Systems, function fields, Homogeneous flows

File Description: application/xml

Access URL: http://arxiv.org/abs/2405.11274
https://zbmath.org/7967038
https://doi.org/10.1016/j.aim.2024.110084

Certain Singular Distributions and Fractals: Certain singular distributions and fractals

Authors: Symon, Serbenyuk

Source: Tatra Mountains Mathematical Publications. 79:163-198

Subject Terms: Fractals, Irrationality, linear independence over a field, fractal, Mathematics - Classical Analysis and ODEs, Moran structure, Extremal combinatorics, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Metric theory of other algorithms and expansions, measure and Hausdorff dimension, Elementary functions, Hausdorff dimension, range of values of a function, continuous function

File Description: application/xml

Access URL: http://arxiv.org/pdf/2005.02485
http://arxiv.org/abs/2005.02485
https://zbmath.org/7460183
https://doi.org/10.2478/tmmp-2021-0026

A generalization of the Erdös–Rényi limit theorem and the corresponding multifractal analysis: A generalization of the Erdős-Rényi limit theorem and the corresponding multifractal analysis

Authors: Min Yu, Haibo Chen

Source: Journal of Number Theory. 192:307-327

Subject Terms: Fractals, regularly varying sequence, Erdős-Rényi limit theorem, Metric theory of other algorithms and expansions, measure and Hausdorff dimension, Hausdorff dimension, 0101 mathematics, 16. Peace & justice, 01 natural sciences, run-length function

File Description: application/xml

Access URL: https://zbmath.org/6943100
https://doi.org/10.1016/j.jnt.2018.04.019
https://www.sciencedirect.com/science/article/pii/S0022314X18301380

Hausdorff dimension and uniform exponents in dimension two

Authors: Bugeaud, Yann, Cheung, Yitwah, Chevallier, Nicolas

Contributors: Chevallier, Nicolas

Source: Mathematical Proceedings of the Cambridge Philosophical Society. 167:249-284

Subject Terms: Continued fractions and generalizations, Mathematics - Number Theory, self-similar coverings, Metric theory of other algorithms and expansions, measure and Hausdorff dimension, singular matrix, Hausdorff dimension, Diophantine approximation in probabilistic number theory, 01 natural sciences, singular vectors, uniform exponent, Simultaneous homogeneous approximation, linear forms, Metric theory, FOS: Mathematics, Number Theory (math.NT), 0101 mathematics, Dirichlet improvable sets, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]

File Description: application/pdf; application/xml

Access URL: http://arxiv.org/pdf/1610.06374
http://arxiv.org/abs/1610.06374
https://arxiv.org/abs/1610.06374
https://arxiv.org/pdf/1610.06374.pdf
http://ui.adsabs.harvard.edu/abs/2016arXiv161006374B/abstract
https://ui.adsabs.harvard.edu/abs/2019MPCPS.167..249B/abstract
https://hal.archives-ouvertes.fr/hal-01381425
https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/hausdorff-dimension-and-uniform-exponents-in-dimension-two/ED5D62D56118A627A6F44EB5AA33ABAA
https://hal.archives-ouvertes.fr/hal-01381425/document

The Hausdorff dimension of level sets described by Erdös–Rényi average: The Hausdorff dimension of level sets described by Erdős-Rényi average

Authors: Haibo Chen, Xinghuo Long, Dao-Xin Ding

Source: Journal of Mathematical Analysis and Applications. 458:464-480

Subject Terms: Moran set, Erdős-Rényi average, Dimension theory of smooth dynamical systems, Metric theory of other algorithms and expansions, measure and Hausdorff dimension, Relations of ergodic theory with number theory and harmonic analysis, Hausdorff dimension, slowly varying sequence, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/6802324
https://doi.org/10.1016/j.jmaa.2017.09.018
https://www.sciencedirect.com/science/article/pii/S0022247X17308478

The waiting spectra of the sets described by the quantitative waiting time indicators

Authors: HaiBo Chen, JunMin Tang

Source: Science China Mathematics. 57:2335-2346

Subject Terms: Fractals, Hausdorff and packing measures, 0202 electrical engineering, electronic engineering, information engineering, Metric theory of other algorithms and expansions, measure and Hausdorff dimension, quantitative waiting time indicator, Hausdorff dimension, 02 engineering and technology, 0101 mathematics, waiting time, 01 natural sciences, cut set

File Description: application/xml

Access URL: https://link.springer.com/content/pdf/10.1007%2Fs11425-014-4854-7.pdf
http://ui.adsabs.harvard.edu/abs/2014ScChA..57.2335C/abstract
https://link.springer.com/article/10.1007/s11425-014-4854-7

$p$-adic path set fractals and arithmetic: \(p\)-adic path set fractals and arithmetic

Authors: William C. Abram, Jeffrey C. Lagarias

Source: Journal of Fractal Geometry, Mathematics of Fractals and Related Topics. 1:45-81

Subject Terms: \(p\)-adic arithmetic, Non-Archimedean dynamical systems, Metric theory of other algorithms and expansions, measure and Hausdorff dimension, Symbolic dynamics, Hausdorff dimension, Metric Geometry (math.MG), finite automata, 11K55, 11S82, 28A80, 37B10, 16. Peace & justice, 01 natural sciences, Fractals, Mathematics - Metric Geometry, 13. Climate action, FOS: Mathematics, 0101 mathematics, graph-directed construction

File Description: application/xml

Access URL: http://www.ems-ph.org/journals/show_pdf.php?issn=2308-1309&vol=1&iss=1&rank=2
http://arxiv.org/abs/1210.2478
https://arxiv.org/abs/1210.2478
https://arxiv.org/pdf/1210.2478.pdf
https://www.ems-ph.org/journals/show_abstract.php?issn=2308-1309&vol=1&iss=1&rank=2
https://ui.adsabs.harvard.edu/abs/2012arXiv1210.2478A/abstract
https://www.ems-ph.org/journals/show_pdf.php?issn=2308-1309&vol=1&iss=1&rank=2

S-expansions in dimension two: \(S\)-expansions in dimension two

Authors: Bernhard Schratzberger

Source: Journal de théorie des nombres de Bordeaux. 16:705-732

Subject Terms: Metric theory of continued fractions, Continued fractions and generalizations, Metric theory of other algorithms and expansions, measure and Hausdorff dimension

File Description: application/xml

Access URL: https://jtnb.centre-mersenne.org/item/10.5802/jtnb.467.pdf
https://zbmath.org/2188538
https://doi.org/10.5802/jtnb.467
http://archive.numdam.org/article/JTNB_2004__16_3_705_0.pdf
https://uni-salzburg.elsevierpure.com/en/publications/s-expansions-in-dimension-two
https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.467/
https://jtnb.centre-mersenne.org/item/10.5802/jtnb.467.pdf
https://eudml.org/doc/249276

Topological and fractal properties of real numbers which are not normal

Authors: Mykola Pratsiovytyi, Sergio Albeverio, Grygoriy Torbin

Source: Bulletin des Sciences Mathématiques. 129:615-630

Subject Terms: Mathematics(all), Hausdorff-Besicovitch dimension, Metric theory of other algorithms and expansions, measure and Hausdorff dimension, normality of real numbers, Transformations preserving the fractal dimension, superfractal set, Q∗-representation of real numbers, 01 natural sciences, Normal numbers, Fractals, Hausdorff and packing measures, Essentially non-normal numbers, Hausdorff–Besicovitch dimension, 0101 mathematics, Non-normal numbers

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/S000744970500028X
https://www.sciencedirect.com/science/article/abs/pii/S000744970500028X
https://core.ac.uk/display/82177494

The limited Rademacher functions and Bernoulli convolutions associated with Pisot numbers

Authors: De-Jun Feng

Source: Advances in Mathematics. 195:24-101

Subject Terms: \(L^q\)-spectrum, Lq-spectrum, Mathematics(all), Metric theory of other algorithms and expansions, measure and Hausdorff dimension, multifractals, Hausdorff dimension, Multifractals, Pisot numbers, product of matrices, 01 natural sciences, Information dimension, information dimension, Product of matrices, PV-numbers and generalizations, other special algebraic numbers, Mahler measure, Fractals, Hausdorff and packing measures, Real-valued functions in general topology, Limited Rademacher functions, limited Rademacher functions, Relations of ergodic theory with number theory and harmonic analysis, Entropy and other invariants, Bernoulli convolutions, 0101 mathematics

File Description: application/xml

Access URL: https://zbmath.org/2189364
https://doi.org/10.1016/j.aim.2004.06.011
http://www.math.cuhk.edu.hk/~djfeng/fengpapers/rademanew/adv-2005.pdf
https://www.sciencedirect.com/science/article/abs/pii/S0001870804002142
https://core.ac.uk/display/82174759
https://www.sciencedirect.com/science/article/pii/S0001870804002142

Infinite ergodic theory for Kleinian groups

Authors: Stratmann, B. O., Stadlbauer, M.

Contributors: Stadlbauer, Manuel, Stratmann, B. O., Stadlbauer, M.

Source: Ergodic Theory and Dynamical Systems. 25:1305-1323

Subject Terms: Geodesic flows in symplectic geometry and contact geometry, limit set, Nonsingular (and infinite-measure preserving) transformations, Markov map, General groups of measure-preserving transformations and dynamical systems, Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.), Poincaré section, Metric theory of other algorithms and expansions, measure and Hausdorff dimension, Quasiconformal methods and Teichmüller theory, etc. (dynamical systems), 16. Peace & justice, 01 natural sciences, geodesic flow, Kleinian groups (aspects of compact Riemann surfaces and uniformization), General groups of measure-preserving transformations, 0101 mathematics, Fuchsian groups and their generalizations (group-theoretic aspects), exponent of convergence

File Description: application/xml

Access URL: https://dialnet.unirioja.es/servlet/articulo?codigo=1245250
https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/abs/infinite-ergodic-theory-for-kleinian-groups/FB83FDAC045A3ECDC56EBE8D43BA940A
https://documat.unirioja.es/servlet/articulo?codigo=1245250
https://resolver.sub.uni-goettingen.de/purl?gro-2/50156
https://resolver.sub.uni-goettingen.de/purl?gro-2/132336

The topological structure of fractal tilings generated by quadratic number systems

Authors: Jörg M. Thuswaldner, Shigeki Akiyama

Source: Computers & Mathematics with Applications. 49:1439-1485

Subject Terms: Radix representation, Metric theory of other algorithms and expansions, measure and Hausdorff dimension, Multi-dimensional shifts of finite type, tiling dynamics, 01 natural sciences, Automata, Connectedness, Computational Mathematics, Fractals, Computational Theory and Mathematics, Combinatorial aspects of tessellation and tiling problems, Modelling and Simulation, Tilings in \(n\) dimensions (aspects of discrete geometry), 0101 mathematics, Tiling, Fractal, digital problems

File Description: application/xml

Access URL: https://zbmath.org/2201728
https://doi.org/10.1016/j.camwa.2004.09.008
https://pure.unileoben.ac.at/portal/en/publications/on-the-topological-structure-of-fractal-tilings-generated-by-quadratic-number-systems(fa05e6c1-878e-4049-93da-ff53c806dbab).html
https://www.sciencedirect.com/science/article/abs/pii/S0898122105001628
https://www.sciencedirect.com/science/article/pii/S0898122105001628
https://core.ac.uk/display/82716234
http://math.tsukuba.ac.jp/~akiyama/papers/cnsnew7.pdf

Fractal properties of singular probability distributions with independent Q*-digits: Fractal properties of singular probability distributions with independent \(Q^{\ast}\)-digits

Authors: Grygoriy Torbin, Sergio Albeverio

Source: Bulletin des Sciences Mathématiques. 129:356-367

Subject Terms: Hausdorff dimension of measure, Billingsley dimension, Fractals, Continuity and singularity of induced measures, fractals, singular probability distributions, Entropy of probability distributions, Metric theory of other algorithms and expansions, measure and Hausdorff dimension, entropy of probability distributions, 0101 mathematics, Singular probability distributions, 01 natural sciences

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/pii/S0007449704001393
https://www.sciencedirect.com/science/article/abs/pii/S0007449704001393

On the exact Hausdorff dimension of the set of Liouville numbers

Authors: L. Olsen, Dave L. Renfro

Source: manuscripta mathematica. 116:157-172

Subject Terms: Fractals, Liouville numbers, Diophantine approximation, 4. Education, Metric theory of other algorithms and expansions, measure and Hausdorff dimension, 0101 mathematics, 10. No inequality, 01 natural sciences, Hausdorff measure

File Description: application/xml

Access URL: https://zbmath.org/2156089
https://doi.org/10.1007/s00229-004-0528-z
https://documat.unirioja.es/servlet/articulo?codigo=2804649
https://rd.springer.com/content/pdf/10.1007%2Fs00229-005-0604-z.pdf
https://rd.springer.com/article/10.1007/s00229-004-0528-z
https://dialnet.unirioja.es/servlet/articulo?codigo=2804649
https://link.springer.com/article/10.1007%2Fs00229-005-0604-z

Metrical results on sums of squares and prime values of the integer parts of sequences

Authors: Paul Rowe

Source: Acta Arithmetica. 118:101-115

Subject Terms: Distribution of primes, two integers simultaneous prime, Metric theory, Metric theory of other algorithms and expansions, measure and Hausdorff dimension, Hausdorff dimension, 0101 mathematics, Distribution of integers with specified multiplicative constraints, 01 natural sciences, metric number theorem, sums of two squares

File Description: application/xml

Access URL: https://www.impan.pl/shop/publication/transaction/download/product/83407?download.pdf
https://ui.adsabs.harvard.edu/abs/2005AcAri.118..101R/abstract
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-aa118-2-1

On the sum of degrees of digits occurring in continued fraction expansions of Laurent series

Authors: Jun Wu

Source: Mathematical Proceedings of the Cambridge Philosophical Society. 138:9-20

Subject Terms: Metric theory of continued fractions, sum of degrees of digits, Continued fractions and generalizations, Approximation in non-Archimedean valuations, Hausforff dimension, Metric theory of other algorithms and expansions, measure and Hausdorff dimension, continued fractions, 0101 mathematics, Laurent series, 01 natural sciences

File Description: application/xml

Access URL: https://zbmath.org/2157959
https://doi.org/10.1017/s0305004104008163
http://www.journals.cambridge.org/abstract_S0305004104008163
https://dialnet.unirioja.es/servlet/articulo?codigo=1105916
https://www.cambridge.org/core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society/article/on-the-sum-of-degrees-of-digits-occurring-in-continued-fraction-expansions-of-laurent-series/9FC2932A8F7B2E3A9592C94501A20F9A
http://ui.adsabs.harvard.edu/abs/2005MPCPS.138....9W/abstract

An inhomogeneous Jarník theorem

Authors: Bugeaud, Yann

Contributors: Thureau, Grégory

Source: Journal d'Analyse Mathématique. 92:327-349

Subject Terms: Lebesgue measure, Diophantine approximation, Metric theory, Metric theory of other algorithms and expansions, measure and Hausdorff dimension, Diophantine approximation in probabilistic number theory, 0101 mathematics, 01 natural sciences, Hausdorff measure, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]

File Description: application/xml

Access URL: http://cds.cern.ch/record/851805/files/cer-002534971.pdf
https://link.springer.com/content/pdf/10.1007/BF02787766.pdf
https://link.springer.com/article/10.1007/BF02787766