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  Jeroen Lamb  
  Martin Rasmussen  
  Dmitry Turaev  
  Sebastian van Strien  
RESEARCHERS
Mike Field
POSTDOCS
Fabrizio Bianchi
Trevor Clark
Nikos Karaliolios
Dongchen Li
Paul Verschueren
Björn Winckler
PHD STUDENTS
Alex Athorne
Sajjad Bakrani Balani
Giulia Carigi
Andrew Clarke
Maximilian Engel
Federico Graceffa
Michael Hartl
Giuseppe Malavolta
Guillermo Olicón Méndez
Cezary Olszowiec
Christian Pangerl
Mohammad Pedramfar
Kalle Timperi
VISITORS
Shangzhi Li
Ole Peters
Camille Poignard
Cristina Sargent
Bill Speares
Kevin Webster
RELATED STAFF
Mauricio Barahona
Davoud Cheraghi
Martin Hairer
Darryl Holm
Xue-Mei Li
Greg Pavliotis

DynamIC Seminars (Complete List)

Name Title Date Time Room
Edson de Faria (University of Sao Paulo)Slow growth and entropy-type invariantsAbstract: We discuss a generalization of topological entropy in which the usual exponential growth-rate function is replaced by an arbitrary gauge func- tion. This generalized topological entropy had previously been described by Galatolo in 2003 – up to a choice of notation in the defining formulas – which in turn is essentially the same as that described by Zhao and Pesin in 2015 (that involves a re-parameterization of time). One of the main motivations for studying this new set of invariants comes from the need to distinguish maps with zero (standard) topological entropy. In such cases, if the dynamics is not equicontinuous, then there exists at least one gauge for which the correspond- ing generalized entropy is positive. After illustrating this simple qualitative criterion, we perform a more quantitative study of the growth of orbits in some low-dimensional examples of zero-entropy maps. Our examples include period-doubling maps in dimension one, and maps of the annulus built from circle homeomorphisms having an exceptional minimal set. This talk is based on joint work with P. Hazard and C. Tresser. Tuesday, 27 February 2018 13:00 Huxley 144
Daniel Meyer (University of Liverpool)Quasispheres and Expanding Thurston mapsAbstract: A quasisymmetric map is one that changes angles in a controlled way. As such they are generalizations of conformal maps and appear naturally in many areas, including Complex Analysis and Geometric group theory. A quasisphere is a metric sphere that is quasisymmetrically equivalent to the standard 2-sphere. An important open question is to give a characterization of quasispheres. This is closely related to Cannon's conjecture. This conjecture may be formulated as stipulating that a group that ``behaves topologically'' as a Kleinian group ``is geometrically'' such a group. Equivalently, it stipulates that the ``boundary at infinity'' of such groups is a quasisphere. A Thurston map is a map that behaves ``topologically'' as a rational map, i.e., a branched covering of the 2-sphere that is postcritically finite. A question that is analog to Cannon's conjecture is whether a Thurston map ``is'' a rational map. This is answered by Thurston's classification of rational maps. For Thurston maps that are expanding in a suitable sense, we may define ``visual metrics''. The map then is (topologically conjugate) to a rational map if and only if the sphere equipped with such a metric is a quasisphere. This talk is based on joint work with Mario Bonk. Tuesday, 27 February 2018 14:00 Huxley 139
Mohammad Pedramfar (Imperial College)TBAAbstract: Tuesday, 6 March 2018 14:00 Huxley 139
Nikos Karaliolios (Imperial College)Normal form theorems in Elliptic and Parabolic dynamicsAbstract: We will discuss some normal form theorems for perturbations of the main examples of elliptic and parabolic dynamics, generalizing the classical theorem due to Arnol'd and Moser, concerning perturbations of Diophantine translations in tori. Such theorems try to establish that the orbit of a certain type of diffeomorphism under the relevant notion of conjugation is locally a closed submanifold of a certain codimension. Subsequently, one tries to interpret the perturbations in transversal directions as perturbations that modify the dynamics of the studied diffeomorphism. More precisely, we will provide a general framework for obtaining such theorems and then apply it in order to obtain normal form theorems in the following settings: 1. that of commuting diffeomorphisms of the torus, close to Simultaneously Diophantine rotations. This provides a new, more general and stronger proof of a theorem by Moser on the simultaneous linearizability of such dynamical systems. 2. that of periodic translations in tori. 3. the case of Resonant Diophantine translations, which is intermediate between the periodic case and the classical normal form theorem. 4. the parabolic mapping of the torus T^2. Tuesday, 13 March 2018 14:00 Huxley 139
Jennifer Creaser (University of Exeter)TBAAbstract: Tuesday, 20 March 2018 14:00 Huxley 139

DynamIC Workshops and Mini-Courses (Complete List)

Title Date Venue
Dynamics, Bifurcations, and TopologyMonday, 14 May 2018 – Sunday, 20 May 2018Imperial College London
One Day of Network DynamicsFriday, 9 February 2018Imperial College London
LMS Network Meeting in Holomorphic DynamicsWednesday, 22 March 2017Imperial College London
Aspects of Dynamical SystemsThursday, 16 March 2017 – Saturday, 18 March 2017Imperial College London

Short-term DynamIC Visitors (Complete List)

NameAffiliationArrivalDepartureHost
Ale Jan Homburg VU University Amsterdam Monday, 5 February 2018 Friday, 2 March 2018 Lamb, Rasmussen

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