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.