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

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

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