Holomorphic Dynamics connecting Geometry, Root-Finding, Algebra, and the Mandelbrot set

Project Information

HOLOGRAM

Grant agreement ID: 695621

DOI 10.3030/695621

Project closed

EC signature date 27 July 2016

Start date 1 October 2016

End date 30 June 2022

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost € 2 312 481,00

EU contribution € 2 312 481,00

Coordinated by

UNIVERSITE D'AIX MARSEILLE
France

Publications

Peer reviewed articles (29)

Finding polynomial roots by dynamical systems – A case study

Author(s): Sergey Shemyakov, Roman Chernov, Dzmitry Rumiantsau, Dierk Schleicher, Simon Schmitt, Anton Shemyakov
Published in: Discrete & Continuous Dynamical Systems - A, Issue 40/12, 2020, Page(s) 6945-6965, ISSN 1553-5231
Publisher: American Institute of Mathematical Sciences
DOI: 10.3934/dcds.2020261

The Dynamics of Complex Box Mappings

Author(s): Trevor Clark, Kostiantyn Drach, Oleg Kozlovski & Sebastian van Strien
Published in: Arnold Mathematical Journal, 2022, ISSN 2199-6792
Publisher: Springer Science+Business Media
DOI: 10.1007/s40598-022-00200-7

Core Entropy of Quadratic Polynomials

Author(s): Dzmitry Dudko, Dierk Schleicher
Published in: Arnold Mathematical Journal, Issue 6/3-4, 2020, Page(s) 333-385, ISSN 2199-6792
Publisher: Springer
DOI: 10.1007/s40598-020-00134-y

Combinatorial properties of Newton maps

Author(s): Russell Lodge, Yauhen Mikulich, Dierk Schleicher
Published in: Indiana University Mathematics Journal, Issue 70/5, 2021, Page(s) 1833-1867, ISSN 0022-2518
Publisher: Indiana University Press
DOI: 10.1512/iumj.2021.70.8588

The Weierstrass-Durand-Kerner root finder is not generally convergent

Author(s): Bernhard Reinke, Dierk Schleicher, Michael Stoll
Published in: Mathematics of Computation, 2022, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3783

Inradius Estimates for Convex Domains in2-Dimensional Alexandrov Spaces

Author(s): Kostiantyn Drach
Published in: Analysis and Geometry in Metric Spaces, Issue 22993274, 2018, Page(s) 165–173, ISSN 2299-3274
Publisher: de Gruyter
DOI: 10.1515/agms-2018-0009

A hyperbolic view of the Seven Circles Theorem

Author(s): Kostiantyn Drach, Richard Evan Schwartz
Published in: The Mathematical Intelligencer, Issue 42 (2020), 2020, Page(s) 61–65, ISSN 0343-6993
Publisher: Springer Verlag
DOI: 10.1007/s00283-019-09952-1

Pacman renormalization and self-similarity of the Mandelbrot set near Siegel parameters

Author(s): Dzmitry Dudko, Mikhail Lyubich, Nikita Selinger
Published in: Journal of the American Mathematical Society, Issue 33/3, 2020, Page(s) 653-733, ISSN 0894-0347
Publisher: American Mathematical Society
DOI: 10.1090/jams/942

Algorithmic aspects of branched coverings II/V: sphere bisets and decidability of Thurston equivalence

Author(s): Laurent Bartholdi, Dzmitry Dudko
Published in: Inventiones mathematicae, Issue 223/3, 2021, Page(s) 895-994, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-020-00995-2

Diverging orbits for the Ehrlich–Aberth and the Weierstrass root finders

Author(s): Reinke, Bernhard
Published in: Proceedings of the American Mathematical Society, 2021, Page(s) 1-12, ISSN 1088-6826
Publisher: American Mathematical Society
DOI: 10.1090/proc/15715

Unicritical laminations

Author(s): Sourav Bhattacharya, Alexander Blokh, Dierk Schleicher
Published in: Fundamenta Mathematicae, Issue 258/2022, 2022, Page(s) 25-63, ISSN 0016-2736
Publisher: Polska Akademia Nauk
DOI: 10.4064/fm18-2-2022

On the efficient global dynamics of Newton’s method for complex polynomials

Author(s): Dierk Schleicher
Published in: Nonlinearity, Issue 2023, 2023, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/acb18e

Archimedean toroidal maps and their minimal almost regular covers

Author(s): Kostiantyn Drach, Yurii Haidamaka, Mark Mixer, Maksym Skoryk
Published in: Ars Mathematica Contemporanea, Issue 18553974, 2019, Page(s) 493–514, ISSN 1855-3974
Publisher: Društvo Matematikov, Fizikov in Astronomov Slovenije, Ljubljana
DOI: 10.26493/1855-3974.1825.64c

Rigidity of Newton dynamics

Author(s): Kostiantyn Drach, Dierk Schleicher
Published in: Advances in Mathematics, Issue issue 408, October 2022, 2022, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2022.108591

Exponential growth of some iterated monodromy groups

Author(s): Mikhail Hlushchanka, Daniel Meyer
Published in: Proceedings of the London Mathematical Society, Issue 116/6, 2018, Page(s) 1489-1518, ISSN 0024-6115
Publisher: Oxford University Press
DOI: 10.1112/plms.12118

Algorithmic aspects of branched coverings

Author(s): Laurent Bartholdi, Dzmitry Dudko
Published in: Annales de la faculté des sciences de Toulouse Mathématiques, Issue 26/5, 2017, Page(s) 1219-1296, ISSN 0240-2963
Publisher: Faculté des Sciences de Toulouse
DOI: 10.5802/afst.1566

Antiholomorphic perturbations of Weierstrass Zeta functions and Green’s function on tori

Author(s): Konstantin Bogdanov, Khudoyor Mamayusupov, Sabyasachi Mukherjee, Dierk Schleicher
Published in: Nonlinearity, Issue 30/8, 2017, Page(s) 3241-3254, ISSN 0951-7715
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6544/aa79cf

A characterization of postcritically minimal Newton maps of complex exponential functions

Author(s): KHUDOYOR MAMAYUSUPOV
Published in: Ergodic Theory and Dynamical Systems, Issue 39/10, 2019, Page(s) 2855-2880, ISSN 0143-3857
Publisher: Cambridge University Press
DOI: 10.1017/etds.2017.137

Algorithmic aspects of branched coverings I/V. Van Kampen’s theorem for bisets

Author(s): Laurent Bartholdi, Dzmitry Dudko
Published in: Groups, Geometry, and Dynamics, Issue 12/1, 2018, Page(s) 121-172, ISSN 1661-7207
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/ggd/441

Newton maps of complex exponential functions and parabolic surgery

Author(s): Khudoyor Mamayusupov
Published in: Fundamenta Mathematicae, Issue 241/3, 2018, Page(s) 265-290, ISSN 0016-2736
Publisher: Polska Akademia Nauk
DOI: 10.4064/fm345-9-2017

Algorithmic aspects of branched coverings IV/V. Expanding maps

Author(s): Laurent Bartholdi, Dzmitry Dudko
Published in: Transactions of the American Mathematical Society, Issue 370/11, 2018, Page(s) 7679-7714, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/7199

A combinatorial classification of postcritically fixed Newton maps

Author(s): KOSTIANTYN DRACH, YAUHEN MIKULICH, JOHANNES RÜCKERT, DIERK SCHLEICHER
Published in: Ergodic Theory and Dynamical Systems, 2019, Page(s) 1-32, ISSN 0143-3857
Publisher: Cambridge University Press
DOI: 10.1017/etds.2018.2

Newton's method in practice: Finding all roots of polynomials of degree one million efficiently

Author(s): Dierk Schleicher, Robin Stoll
Published in: Theoretical Computer Science, Issue 681, 2017, Page(s) 146-166, ISSN 0304-3975
Publisher: Elsevier BV
DOI: 10.1016/j.tcs.2017.03.025

Internal Addresses of the Mandelbrot Set and Galois Groups of Polynomials

Author(s): Dierk Schleicher
Published in: Arnold Mathematical Journal, Issue 3/1, 2017, Page(s) 1-35, ISSN 2199-6792
Publisher: Springer Nature
DOI: 10.1007/s40598-016-0042-x

Hausdorff dimension of biaccessible angles for quadratic polynomials

Author(s): Henk Bruin, Dierk Schleicher
Published in: Fundamenta Mathematicae, Issue 238/3, 2017, Page(s) 201-239, ISSN 0016-2736
Publisher: Polska Akademia Nauk
DOI: 10.4064/fm276-6-2016

A sausage body is a unique solution for a reverse isoperimetric problem

Author(s): Roman Chernov, Kostiantyn Drach, Kateryna Tatarko
Published in: Advances in Mathematics, Issue 353, 2019, Page(s) 431-445, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2019.07.005

Algorithmic aspects of branched coverings III/V. Erasing maps, orbispaces, and the Birman exact sequence

Author(s): Laurent Bartholdi, Dzmitry Dudko
Published in: Groups, Geometry, and Dynamics, Issue 2021, 2021, ISSN 1661-7207
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/ggd/629

Puzzles and the Fatou–Shishikura injection for rational Newton maps

Author(s): Kostiantyn Drach, Russell Lodge, Dierk Schleicher, Maik Sowinski
Published in: Transactions of the American Mathematical Society, Issue 374/4, 2021, Page(s) 2753-2784, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/8273

Homotopy Hubbard trees for post-singularly finite exponential maps

Author(s): DAVID PFRANG, MICHAEL ROTHGANG, DIERK SCHLEICHER
Published in: Ergodic Theory and Dynamical Systems, Issue October 2021, 2021, Page(s) 1-46, ISSN 0143-3857
Publisher: Cambridge University Press
DOI: 10.1017/etds.2021.103

Book chapters (1)

A classification of postcritically finite Newton maps

Author(s): Russel Lodge, Yauhen Mikulich, Dierk Schleicher
Published in: In the Tradition of Thurston II, Issue August 2022, 2022, Page(s) 421–448, ISBN 978-3-030-97559-3
Publisher: Springer Verlag
DOI: 10.1007/978-3-030-97560-9_13

Non-peer reviewed articles (1)

John Conway: The Man Who Played Mathematics

Author(s): Dierk Schleicher
Published in: The Mathematical Intelligencer, Issue 43/2, 2021, Page(s) 79-91, ISSN 0343-6993
Publisher: Springer Verlag
DOI: 10.1007/s00283-021-10073-x