MATH401-21S2 (C) Semester Two 2021

Dynamical Systems

15 points

Details:
Start Date: Monday, 19 July 2021
End Date: Sunday, 14 November 2021
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 1 August 2021
  • Without academic penalty (including no fee refund): Friday, 1 October 2021

Description

Dynamical Systems

Dynamical systems sits at the interface of pure and applied mathematics, containing some beautiful theory, as well as applications in diverse fields including numerical analysis, biological systems, economics and medicine.

It is often difficult or impossible to write down an exact solution to systems of nonlinear equations. The emphasis in this course will be on qualitative techniques for classifying the behaviour of nonlinear systems, without necessarily solving them exactly. Two main types of dynamical systems
will be studied: discrete systems, consisting of an iterated map; and continuous systems, consisting of nonlinear differential equations.

Topics covered will include: bifurcations and chaotic behaviour of interval maps; symbolic dynamics; topological model of chaos; mass transport and probabilistic dynamics; phase portrait analysis (Hartman-Grobman theorem, hyperbolicity of limit cycles, invariant manifolds, global bifurcations); centre manifolds.

This course is independent of MATH363 Dynamical Systems, although previous enrolment
there is desirable.

Prerequisites

Subject to approval of the Head of School.

Course Coordinator / Lecturer

Rua Murray

Indicative Fees

Domestic fee $1,000.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All MATH401 Occurrences

  • MATH401-21S2 (C) Semester Two 2021
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