Carmin.tv

Mathematics
and Interactions

Please leave your feedback in order for us to improve your experience !
Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday
15 videos

Arithmetic Geometry – A Conference in Honor of Hélène Esnault on the Occasion of Her 70th Birthday

Multidimensional symbolic dynamics and lattice models of quasicrystals / Dynamique symbolique multidimensionnelle et modèles de quasi-cristaux sur réseau
5 videos

Multidimensional symbolic dynamics and lattice models of quasicrystals / Dynamique symbolique multidimensionnelle et modèles de quasi-cristaux sur réseau

Not Only Scalar Curvature Seminar
58 videos

Not Only Scalar Curvature Seminar

Clément Delcamp : Topological Symmetry and Duality in Quantum Lattice Models
2 videos

Clément Delcamp : Topological Symmetry and Duality in Quantum Lattice Models

All the collections
CIMPA
CIRM
IHES
IHP
LMR
SMF
All the institutions
Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe

Collection Advancing Bridges in Complex Dynamics / Avancer les connections dans la dynamique complexe

Organizer(s) Benini, Anna Miriam ; Drach, Kostiantyn ; Dudko, Dzmitry ; Hlushchanka, Mikhail ; Schleicher, Dierk
Date(s) 20/09/2021 - 24/09/2021
linked URL https://conferences.cirm-math.fr/2546.html
00:00:00 / 00:00:00
22 27

Box renormalization as a 'black box'

By Kostiantyn Drach

The concept of a complex box mapping (or puzzle mapping) is a generalization of the classical notion of polynomial-like map to the case when one allows for countably many components in the domain and finitely many components in the range of the mapping. In one-dimensional dynamics, box mappings appear naturally as first return maps to certain nice sets, and hence one arrives at a notion of box renormalization. We say that a rational map is box renormalizable if the first return map to a well-chosen neighborhood of the set of critical points (intersecting the Julia set) has a structure of a box mapping. In our talk, we will discuss various features of general box mappings, as well as so-called dynamically natural box mappings, focusing on their rigidity properties. We will then show how these results can be used almost as 'black boxes' to conclude similar rigidity properties for box renormalizable rational maps. We will give several examples to illustrate this procedure, these examples include, most prominently, complex polynomials of arbitrary degree and their Newton maps. (The talk is based on joint work with Trevor Clark, Oleg Kozlovski, Dierk Schleicher and Sebastian van Strien.)

Information about the video

Citation data

  • DOI 10.24350/CIRM.V.19811903
  • Cite this video Drach, Kostiantyn (23/09/2021). Box renormalization as a 'black box'. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19811903
  • URL https://dx.doi.org/10.24350/CIRM.V.19811903

Domain(s)

Bibliography

  • CLARK, Trevor, DRACH, Kostiantyn, KOZLOVSKI, Oleg, et al. The dynamics of complex box mappings. arXiv preprint arXiv:2105.08654, 2021. - https://arxiv.org/abs/2105.08654
  • DRACH, Kostiantyn et SCHLEICHER, Dierk. Rigidity of Newton dynamics. arXiv preprint arXiv:1812.11919, 2018. - https://arxiv.org/abs/1812.11919v2
  • DRACH, Kostiantyn, LODGE, Russell, SCHLEICHER, Dierk, et al. Puzzles and the Fatou–Shishikura injection for rational Newton maps. Transactions of the American Mathematical Society, 2021, vol. 374, no 4, p. 2753-2784. - https://doi.org/10.1090/tran/8273
  • DRACH, Kostiantyn, MIKULICH, Yauhen, RÜCKERT, Johannes, et al. A combinatorial classification of postcritically fixed Newton maps. Ergodic Theory and Dynamical Systems, 2019, vol. 39, no 11, p. 2983-3014. - https://doi.org/10.1017/etds.2018.2

MSC codes

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow




Register

  • Bookmark videos
  • Add videos to see later &
    keep your browsing history
  • Comment with the scientific
    community
  • Get notification updates
    for your favorite subjects
Copyright Carmin.tv 2024
By browsing our website, you accept the use of cookies to improve your experience. Find out more about our privacy policy.
Approve
Give feedback