STAFF
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|
| Name |
Title |
Date |
Time |
Room |
| Mike Todd (St Andrews) | Phase transitions and limit lawsAbstract: The `statistics’ of a dynamical system is the collection of statistical limit laws it satisfies. This starts with Birkhoff’s Ergodic Theorem, which is about averages of some observable along orbits: this is a pointwise result, for typical points for a given invariant measure. Then we can look for forms of Central Limit Theorem, Large Deviations and so on: these are about how averages fluctuate, globally, with respect to the invariant measure.
In this talk I’ll show how the form of the `pressure function' for a dynamical system determines its statistical limit laws. This is particularly interesting when the system has slow mixing properties, or, even more extreme, in the null recurrent case (where the relevant invariant measure is infinite). I’ll start by introducing these ideas for simple interval maps with nice Gibbs measures and then indicate how this generalises. This is joint work with Henk Bruin and Dalia Terhesiu. |
Tuesday, 23 October 2018 |
14:00 |
Huxley 130 |
| Xavier Buff (University of Toulouse) | Irreducibility in holomorphic dynamicsAbstract: We study the irreducibility (over Q or over C) of various loci defined dynamically. For example,
given an integer d>=2, consider the space of polynomials f_a(z) = a z^d+1. Is the set of parameters
a such that 0 is periodic with period n irreducible over Q ? As another example, consider the space of
cubic polynomials f_{b,c} which have a critical point at 0 with associated critical value 1 and a critical point
c different from 0 with critical value b different from 1. Is the set of parameters (b,c) such that 0 is
periodic with period n irreducible over C ? |
Tuesday, 30 October 2018 |
14:00 |
Huxley 130 |
| Ian Melbourne (University of Warwick) | Anomalous diffusion in deterministic Lorentz gasesAbstract: The classical Lorentz gas model introduced by Lorentz in 1905, studied further by Sinai in the 1960s, provides a rich source of examples of chaotic dynamical systems with strong stochastic properties (despite being entirely deterministic). Central limit theorems and convergence to Brownian motion are well understood, both with standard n^{1/2} and nonstandard (n log n)^{1/2} diffusion rates.
In joint work with Paulo Varandas, we discuss examples with diffusion rate n^{1/a}, 1 |
Tuesday, 6 November 2018 |
14:00 |
Huxley 130 |
| Daniel Meyer (University of Liverpool) | TBAAbstract: TBA |
Tuesday, 13 November 2018 |
14:00 |
Huxley 130 |
| Matthew Jacques (The Open University) | TBAAbstract: TBA |
Tuesday, 20 November 2018 |
14:00 |
Huxley 130 |
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