Home
Publications
Undergraduates
Postgraduates
Postdocs
Calendar
Contact
STAFF
Jeroen Lamb
Martin Rasmussen
Dmitry Turaev
Sebastian van Strien
HONORARY STAFF
Boumediene Hamzi
Tiago Pereira
POSTDOCS
Bernat Bassols Cornudella
Konstantinos Kourliouros
Iacopo Longo
Giuseppe Tenaglia
Wei Hao Tey
Jingdong Zhang
PHD STUDENTS
Chris Chalhoub
Michal Fedorowicz
Emilia Gibson
Vincent Goverse
Amir Khodaeian Karim
Chek Lau
Ziyu Li
Tianyi Liu
Dmitrii Mints
John Parry
VISITORS
Ole Peters
Cristina Sargent
Bill Speares
RELATED STAFF
Mauricio Barahona
Davoud Cheraghi
Martin Hairer
Darryl Holm
Xue-Mei Li
Greg Pavliotis
Kevin Webster
DynamIC Seminars
(
Complete List
)
Name
Title
Date
Time
Room
Victor Kleptsyn (Institut de Recherche Mathématique de Rennes)
Rotation numbers of skew products and their dependence on a parameter
Abstract:
Given a skew product over an ergodic transformation with the circle as the fiber, one can define the associated (fiberwise) rotation number. If the skew product depends continuously on a parameter, then so does the rotation number; my talk with be devoted to the regularity of this dependence. This question is motivated, in particular, by the study of the discrete Schrödinger operator with dynamically defined potential. For such an operator, the distribution function of the density of states measure (DOS) is exactly the rotation number of the associated S^1-cocycle as a function of energy as a parameter. I will present two results: 1) The rotation number is (under very mild assumptions) log-Hölder; this is a joint result with Anton Gorodetski (https://doi.org/10.1017/etds.2025.10195). This statement provides a dynamical viewpoint on the Craig-Simon theorem, stating the log-Hölder regularity for the DOS. 2) It turns out that the increment of the rotation number can be expressed in terms of invariant measures of the skew products (with the corresponding parameter values). For the random dynamics with i.i.d. maps, this gives a formula for the increment of the rotation number in terms of (forward and backward) stationary measures of the dynamics. This integral formula explains the analogy between known results on the regularity of DOS and stationary measures: the rotation number is at least as regular as the stationary measures (at least up to C^1 regularity). This is a joint work with Pedro Duarte and Anton Gorodetski (https://arxiv.org/abs/2512.00195).
Tuesday, 30 June 2026
11:00
HXLY 130
DynamIC Workshops and Mini-Courses
(
Complete List
)
Title
Date
Venue
One-day workshop on Random Dynamical Systems and Ergodic Theory
Tuesday, 9 September 2025
HXLY 340, Imperial College London
CHAOS (Homoclinic Bifurcations, Strange Attractors, Arnold Diffusion, Fermi Acceleration, Solitons)
Sunday, 24 September 2023 – Friday, 29 September 2023
Nesin Math Village, Izmir, Turkey
Short-term DynamIC Visitors
(
Complete List
)
Name
Affiliation
Arrival
Departure
Host
No visitors scheduled currently
Links
