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Publications and preprints of Bernd O. Stratmann

(see also MathSciNet and/or ZMath)

Preprints.

`Upper estimates for stable dimensions of fractal sets with variable numbers of foldings',
(with E. Mihailescu );
preprint (pdf), accepted by International Mathematics Research Notices.
`Geometric renormalisation and Hausdorff dimension for loop-approximable geodesics escaping to infinity',
(with K.H. Falk);
preprint in arXiv:org/pdf.

Recent Publications.

`A Frechet law and an Erdös-Philipp law for maximal cuspidal windings',
(with J. Jaerisch and M. Kesseböhmer);
preprint in arXiv:org/pdf
Ergodic Theory & Dynamical Systems 33 , issue 04, (2013) page 1008-1028; doi:10.1017/S0143385712000235
`A dichotomy between uniform distributions of the Stern--Brocot and the Farey sequence',
(with M. Kesseböhmer);
preprint in arXiv:org/pdf.
Uniform Distribution Theory 07, no. 2, (2012) page 21-33.
`From Farey and Gauss to modern times, and variations of the theme',
Report on Oberwolfach Mini-Workshop: Thermodynamic Formalism, Geometry and Stochastics (2012), doi: 10.4171/OWR/2012/03.
`Strong renewal theorems and Lyapunov spectra for alpha--Farey and alpha--Lüroth systems',
(with M. Kesseböhmer and S. Munday);
preprint in arXiv:org/pdf
Ergodic Theory & Dynamical Systems 32 (2012) page 989-1017; doi:10.1017/S0143385711000186
`On the asymptotic behaviour of the Lebesgue measure of sum-level sets for continued fractions',
(with M. Kesseböhmer);
preprint in arXiv:org/pdf ;
Discrete and Continuous Dynamical Systems - Series A (DCDS-A) Vol. 32, no. 7 (2012) page 2437-2451; doi:10.3934/dcds.2012.32.2437
`The Patterson measure: classics, variations and applications',
(with M. Denker); preprint (pdf);
published in: Contributions to Analytic and Algebraic Number Theory - Festschrift for S. J. Patterson, , page 171-197, 2012, Spinger Verlag.
`A note on the algebraic growth rate of Poincare series for Kleinian groups',
(with M. Kesseböhmer); preprint in arXiv:org/pdf;
published in: Contributions to Analytic and Algebraic Number Theory - Festschrift for S. J. Patterson, page 237-247, 2012, Spinger Verlag; doi:10.1007/978-1-4614-1219-9_10
`Checking atomicity of conformal ending measures for Kleinian groups',
(with K.H. Falk and K. Matsuzaki);
preprint in arXiv:org/pdf ;
Conformal Geometry and Dynamics 14 (2010) page 167-183.
`Sets of non-differentiability for conjugacies between expanding interval maps',
(with T. Jordan, M. Kesseböhmer and M. Pollicott);
(dedicated to Michal Misiurewicz on the occasion of his 60th birthday);
preprint in arXiv:org/pdf
Fundamenta Matemathicae 206 (2009) page 161-183. doi: 10.4064/fm206-0-10(2009).
`The Hausdorff dimension of the set of dissipative points for a Cantor-like model set for singly cusped parabolic dynamics',
(with J. Schmeling);
preprint in arXiv:org/pdf and ESI Preprints 2008, No. 1999;
Kodai Mathematical Journal 32 (2) (2009) page 179-196. (pdf).
`Hölder-differentiability of Gibbs distribution functions',
(with M. Kesseböhmer); preprint in arXiv:org/pdf and Oberwolfach Preprints 2007 .
Mathematical Proceedings Cambridge Philosophical Society 147, no. 2 (2009) page 489-503. doi:10.1017/S0305004109002473.
`Fractal analysis for sets of non-differentiability of Minkowski's question mark function',
(with M. Kesseböhmer); (preprint in arXiv:org/pdf );
Journal of Number Theory 128 (9) (2008) page 2663-2686, doi:10.1016/j.jnt.2007.12.010; doi:10.1017/S0305004109002473
`Refined measurable rigidity and flexibility for conformal iterated function systems',
(with M. Kesseböhmer); (preprint in arXiv:math.DS/0603571 );
New York Journal of Mathematics 14 (2008) page 33-51.
`Homology at infinity; fractal geometry of limiting symbols for modular subgroups',
(with M. Kesseböhmer); (abstract);
(preprint under the title `Limiting modular symbols and their fractal geometry' in arXiv:math.GT/0611048 );
Topology 46 (5) (2007) page 469-491, doi:10.1016/j.top.2007.03.004.
`Lyapunov spectra for KMS states on Cuntz--Krieger algebras',
(with M. Kesseböhmer and M. Stadlbauer); (abstract)- (preprint in arXiv:math.DS/0601354 );
Mathematische Zeitschrift 256 (4) (2007) page 871-893, doi: 10.1007/s00209-007-0110-y.
`Pseudo-Markov systems and infinitely generated Schottky groups',
(with M. Urbanski); (abstract);
American Journal of Mathematics vol. 129 (4) (2007) page 1019-1062.
`A multifractal analysis for Stern-Brocot internals, continued fractions and Diophantine growth rates',
(with M. Kesseböhmer); (preprint in arXiv:math.NT/0509603);
Journal für die reine und angewandte Mathematik (Crelle's Journal) 605 (2007) page 133-163; doi: 10.1515/CRELLE.2007.029
`Diophantine extremality of the Patterson measure' dvi,
(with M. Urbanski);
Mathematical Proceedings of the Cambridge Philosophical Society 140, Part 2 (2006) page 297-304; doi: 10.1017/S0305004105009114
`A remark on densities of hyperbolic dimensions for conformal iterated function systems with applications to conformal dynamics and fractal number theory' pdf;
(with M. Stadlbauer);
Indagationes Math. 17 (2006) page 311-317; doi:10.1016/S0019-3577(06)80024-8
`Fractal geometry on hyperbolic manifolds' pdf, (survey article, refereed);
Non-Euclidean Geometries, Janos Bolyai Memorial Volume, (eds. A. Prekopa and E. Molnar); Springer Verlag, (2006) page 227-249; ISBN: 0387295542
`Constructing restricted Patterson measures for geometrically infinite Kleinian groups';
(with K.H. Falk ); (abstract);
Acta Mathematica Sinica, 22 (No. 2) (2006) page 431-446 (Springer-Verlag Heidelberg); doi: 10.1007/s10114-005-0626-1

In Preparation.

`Remarks on slippery Devil's staircases',
(with M. Kesseböhmer).
`Non-commutative geometry and multifractal formalism',
(with M. Kesseböhmer and M. Stadlbauer).

Further Publications.

MATHEMATICA GOTTINGENSIS

`Infinite ergodic theory for Kleinian groups' pdf,
(with M. Stadlbauer),
Ergodic Theory & Dynamical Systems 25 (2005) page 1305-1323; doi: 10.1017/S014338570400104X
`Remarks on Hausdorff dimensions for transient limit sets of Kleinian groups' pdf,
(with K.H. Falk),
Tohoku Mathematical Journal 56 (4) (2004) page 571-582; (abstract); doi: 10.2748/tmj/1113246751
`Metrical Diophantine analysis for tame parabolic iterated function systems' pdf,
(with M. Urbanski)
Pacific Journal of Mathematics 216 (2) (2004) page 261-292. - (abstract article)
`A multifractal formalism for growth rates and applications to geometrically finite Kleinian groups' ps,
(with M. Kesseböhmer),
Ergodic Theory & Dynamical Systems 24 (1) (2004) page 141-170. (abstract). doi: 10.1017/S0143385703000282
`The exponent of convergence of Kleinian groups; on a Theorem of Bishop and Jones' pdf,
Proceedings of the Conference `Fractal Geometry and Stochastics' (Friedrichroda, Germany, 2003);
Progress in Probability 57 (2004) page 93-107. (abstract), ISBN: 0817652639
`Mulifractal analysis of parabolically semihyperbolic generalized polynomial-like maps' dvi,
(with M. Urbanski),
IP New Studies in Advanced Mathematics 5 (2004) page 393-347. (abstract).
`Stern-Brocot pressure and multifractal spectra in ergodic theory of numbers' pdf,
(with M. Kesseböhmer),
Stochastics and Dynamics 4 (1) (2004) page 77-84; doi:10.1142/S0219493704000948
`Real analyticity of topological pressure for parabolically semihyperbolic generalized polynomial-like maps' dvi,
(with M. Urbanski),
Indagationes Math., N.S. 14 (1) (2003) page 119-134; (abstract); doi:10.1016/S0019-3577(03)90075-9
`A note on geometric upper bounds for the exponent of convergence of convex cocompact Kleinian groups' ,
Indagationes Math., N.S., 13 (2) (2002) page 269-280; (abstract); doi:10.1016/S0019-3577(02)80010-6
`Jarnik and Julia; a Diophantine analysis for parabolic rational maps',
(with M. Urbanski),
Mathematica Scandinavica 91 (2002) page 27-54; ( abstract -- article).
`Well-approximable points for Julia sets with parabolic and critical points',
(with M. Urbanski and M. Zinsmeister),
Computational Methods and Function Theory, 1 (1), 3 (2001) page 87 - 97; (abstract --article).
`Hausdorff dimension 2 for Julia sets of quadratic polynomials',
(with S.-M. Heinemann),
(abstract);
Mathematische Zeitschrift 237 (2001) page 571�583; doi: 10.1007/s002090100231
`Kleinian groups with singly cusped parabolic fixed points',
(with J.R. Parker),
Kodai Journal of Mathematics 24 (2001) page 169-206; (abstract article).
`Geometric exponents for hyperbolic Julia sets',
(with S.-M. Heinemann),
Illinois Journal of Mathematics 45 No. 3 (2001) page 775-785; (abstract -- article).
`The geometry of conformal measures for parabolic rational maps',
(with M. Urbanski),
Mathematical Proceedings of the Cambridge Philosophical Society 128 (2000) page 141-156; (abstract); doi: 10.1017/S0305004199003837
`Weak singularity spectra of the Patterson measure for geometrically finite Kleinian groups with parabolic elements',
Michigan Mathematical Journal 46 (1999) page 573-587; (abstract); doi: 10.1307/mmj/1030132480
Book Review of `Hyperbolic Manifolds and Kleinian Groups' by K. Matsuzaki and M. Taniguchi,
(Oxford Mathematical Monograph, Clarendon Press, 1998),
in Proceedings of the Edinburgh Mathematical Society 42 (1999) page 655.
`Fractal dimensions for dissipative sets',
(with R. Vogt),
Nonlinearity 10 (1997) page 565-577; (abstract); doi:10.1088/0951-7715/10/2/014
`A remark on Myrberg initial data for Kleinian groups',
Geometriae Dedicata 65 (1997) page 257-266; (abstract); doi: 10.1023/A:1004933005742
`The Hausdorff dimension of bounded geodesics on geometrically finite manifolds',
Ergodic Theory & Dynamical Systems 17 (1997) page 227-246; (abstract); doi: 10.1017/S0143385797069800
`Multiple fractal aspects of conformal measures; a survey',
Proceedings of the Workshop `Fractals and Dynamics' (eds. M. Denker, S.-M. Heinemann, B.O. Stratmann),
Mathematica Gottingensis 5 (1997) page 65-71; (abstract).
`The box-counting dimension for geometrically finite Kleinian groups',
(with M. Urbanski),
Fundamenta Mathematicae 149 (1996) page 83-93; (abstract).
`Fractal dimensions for Jarnik limit sets of geometrically finite Kleinian groups; the semi-classical approach',
Arkiv för Matematik 33 (1995) page 385-403; (abstract).
`A note on counting cuspidal excursions',
Annales Academiae Scientiarum Fennicae 20 (1995) page 359-372; (abstract).
`The Patterson measure for geometrically finite groups with parabolic elements, new and old',
(with S. Velani),
Proceedings of the London Mathematical Society (3) 71 (1995) page 197-220; (abstract).
`Diophantine approximation in Kleinian groups',
Mathematical Proceedings of the Cambridge Philosophical Society 116, Part 1 (1994) page 57-78; (abstract).