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Name 
Title 
Date 
Time 
Room 
Edson de Faria (University of Sao Paulo)  Slow growth and entropytype invariantsAbstract: We discuss a generalization of topological entropy in which the
usual exponential growthrate 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 reparameterization 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 lowdimensional examples of zeroentropy maps. Our examples include
perioddoubling 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 2sphere. 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 2sphere 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 MiniCourses (Complete List)
Shortterm DynamIC Visitors (Complete List)
Name  Affiliation  Arrival  Departure  Host  Ale Jan Homburg  VU University Amsterdam  Monday, 5 February 2018  Friday, 2 March 2018  Lamb, Rasmussen 
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