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DynamIC Seminars (Complete List)

Name Title Date Time Room
Maximilian Engel (TU Munich)A random dynamical systems perspective on isochronicity for stochastic oscillationsAbstract: For an attracting periodic orbit (limit cycle) of a deterministic dynamical system, one defines isochrons as the cross-sections of the orbit with fixed return time under the flow, or, equivalently, as the stable manifolds foliating neighborhoods of the limit cycle. In recent years, there has been a lively discussion in the mathematical physics community on how to define isochrons for stochastic oscillations, i.e. limit cycles or heteroclinic cycles exposed to stochastic noise. The main discussion has concerned an approach finding stochastic isochrons as sections of equal expected return times versus the idea of considering eigenfunctions of the backward Kolmogorov operator.
We introduce a new rigorous definition of stochastic isochrons as random stable manifolds for random periodic solutions with noise-dependent period. This allows us to introduce a random version of isochron maps whose level sets coincide with the random stable manifolds. Furthermore, we sketch how this random dynamical systems interpretation may be linked to the physics approaches by appropriate averaging.
Tuesday, 25 February 2020 13:00 HXLY 342
Stergios Antonakoudis (Imperial College)Fixed point theorems for holomorphic maps on Teichmüller spaces and beyond.Abstract: Studying the existence of fixed points for holomorphic maps on Teichmüller spaces serves as a framework for proving 'geometrization' theorems, such as Thurston's topological characterisation of hyperbolic 3-manifolds. In this talk, we will prove a general theorem addressing the existence of fixed points for holomorphic maps on Teichmüller spaces and a more general class of complex domains by focusing on the intrinsic shape of these domains and leveraging a novel idea that combines arguments from (complex) geometry and elementary combinatorics. We'll also discuss a geometric generalisation and possible applications, obtained by a distillation of the ideas and arguments involved in the proofs. Tuesday, 3 March 2020 13:00 HXLY 342
Vladislav Sidorenko (Keldysh Institute of Applied Mathematics)The Eccentric Kozai-Lidov Effect as a Resonance PhenomenonAbstract: Considering the evolution of a weakly perturbed Keplerian motion under the scope of the restricted three-body problem M.L.Lidov (1961) and Y.Kozai (1962) discovered independently coupled oscillations of eccentricity and inclination (KL-cycles). Their classical investigations were based on the integrable model of the secular evolution obtained after double averaging of the disturbing function approximated by the first non-trivial term (more precisely, by the quadruple term) in the series expansion with respect to the ratio of semimajor axis of the disturbed body and the disturbing body.
If the next (octupole) term is kept in the expression of the disturbing function, then the longterm modulation of the KL-cycles can be established (Ford et al., 2000; Katz et al., 2011; Lithwick, Naoz, 2011). In particular, the flips become possible from prograde to retrograde orbit and back again. Since flips are observed only in the case of the disturbing body motion in the orbit with non-zero eccentricity, the term “Eccentric Kozai-Lidov Effect” (or EKL-effect) was proposed in (Lithwick, Naoz, 2011) to specify such a dynamical behavior.
We demonstrate that the EKL-effect can be interpreted as a resonance phenomenon. With this aim we write down the motion equations in terms of the “action-angle” variables provided by the integrable Kozai-Lidov model. It turns out that for some initial values the resonance is degenerate and the usual “pendulum” approximation is insufficient to describe the evolution of the resonance phase. The analysis of the related bifurcations allows us to estimate the typical time between the successive flips for different parts of the phase space.
Tuesday, 10 March 2020 13:00 HXLY 342
Olga Lukina (University of Vienna)tbaAbstract: tba Tuesday, 17 March 2020 14:00 HXLY 140
Toby Hall (University of Liverpool)tbaAbstract: tba Tuesday, 2 June 2020 13:00 HXLY 139

DynamIC Workshops and Mini-Courses (Complete List)

Title Date Venue
Workshop on Critical Transitions in Complex SystemsMonday, 25 March 2019 – Friday, 29 March 2019Imperial College London

Short-term DynamIC Visitors (Complete List)

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