One-dimensional dynamics, spring 2014

Lecturer

Neil Dobbs

Scope

5 sp.

Type

Advanced studies

Prerequisites

This course will draw on general mathematical culture. Familiarity with Lebesgue integration, elementary topology, weak-* convergence and basic complex analysis would certainly be helpful, but are not essential.

Description

In dynamical systems, one aspires to describe long-term, qualitative behaviour of systems that evolve with time according to some rule. Even simple evolution rules may lead to a rich variety of possible long-term behaviour with "sensitive dependence on initial conditions". We shall study how points move around on an interval or in the complex plane, where the evolution rule is given by a function from the space to itself.

Topics covered will include fractals, ergodicity, Sharkovskii's Theorem, continued fractions and rotation numbers, Julia sets (in the complex plane) and more. There will be links to probability, number theory, physics and ecology. We shall use some basic topology, combinatorics, measure theory, analysis and mathematical intuition.

Lectures

Weeks 3-9 and 11-18, Thursday 10-12 in room B322.

Easter Holiday 17.-23.4. 

There will be exercise sessions on Tuesday mornings, 10-12, C129, starting week 4.

Exams

Bibliography

Registration

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