# Semester 1, 2011 - 2012. MA50215: Specialist Reading Course

**Symmetric Bifurcation Theory**

This is a reading course in bifurcation theory in the presence of symmetry. We will begin by following
the book by Hoyle.

R.B. Hoyle,

*Pattern Formation: an introduction to methods.* CUP, Cambridge. (2006)

### Course details

Week 1 - 3 (6 - 26 Feb): Definitions: group, group presentation, subgroup, coset. Lagrange's theorem. Normal subgroups and quotient groups. Examples: Z_4, Z_6, Z_n, D_4.

Week 4 (27 Feb): Hoyle, chapter 3. Exercises 3.1 - 3.9.

Week 5 (5 March). Hoyle, chapter 4. Sections 4.1 - 4.4 inclusive, i.e. pages 85 -122. Exercises 4.1 - 4.7. Section 4.3 of my notes: representations.

Week 6 (12 March). Sections 4.4 and 4.5 of my notes: Symmetric ODEs and bifurcations; the Equivariant Branching Lemma. Section 4.6(i): Steady-state bifurcation with D_3 symmetry. Homework: question 6 from the problem sheet.

Week 7 (19 March). Sections 4.6 (worked examples) and 4.7 (Equivariant Hopf Theorem).

Week 8 (26 March).

Week 9 (16 April).

Week 10 (23 April).

Week 11 (30 April).

Meetings.

**1. Tuesday 21 February at 11.15. Hand in work by noon on the previous day.**

**2. Tuesday 28 February at 11.15. Hand in work by noon on the previous day.**

**3. Tuesday 6 March at 11.15. Hand in work by noon on the previous day.**

**4. Tuesday 13 March at 11.15. Hand in work by noon on the previous day.**

**5. Monday 26 March at 11.15.**

**6. Tuesday 17 April at 11.15. Hand in work by noon on the previous day.**