FALL SEMESTER 2004
MATH642 - Introduction to Dynamical Systems-1
HOMEWORK ASSIGNMENTS.

Text M. Brin and G. Stuck, Introduction to Dynamical Systems

Hk refers to problems from homework file
Section Problems Extra credit Problems Due
1.2 Circle Rotations 1.2.1, 1.2.2, 1.2.3 1.2.4 Sept. 14
1.3 Expanding Maps 1.3.2, 1.3.3, 1.3.4 1.3.5 Sept. 14
1.3 Expanding Maps H1 Sept. 18
1.7 Toral automorhisms 1.7. 1, H2 H3 Sept. 18
1.4 Shifts and subshifts 1.4. 1, 1.4.4, 1.4.5 Sept. 28
1.6 Gauss map H4, H6 H5 Sept. 28
1.5 Quadratic maps 1.5.4, 1.5.5, 1.5.6 Oct. 2
1.11 Suspension and cross section 1.11.2, H7 1.11.3 Oct. 2
2.1 Recurrence 2.1.3 2.1.11 Oct. 9
2.2 Topological Transitivity 2.2.3, 2.2.5 2.2.6 Oct. 9
2.2 Topological Mixing 2.3.2, 2.3.3 Oct. 9
2.4 Expansive transformations. H8, H9 Oct. 16
2.5 Topological entropy 2.5.4, 2.5.6 2.5.7 Oct. 16
2.6 Computing topological entropy 2.6.1, H10 Oct. 16
3.1 Subshifts and codes 3.1.1, 3.1.3 Oct. 26
3.2 Subshifts of finite type 3.2.1, 3.2.4 3.2.2 Oct. 26
3.3 Perron-Frobenius Theorem 3. 3.2, H11, H12, H13 Oct. 26
3.4 Dynamical zeta function 3.4.3, 3.4.4, 3.4.5, 3.4.6 3.4.7 Oct. 30
3.6 Substitutions H14 Nov. 6
3.7 Sofic shifts H15, 3.7.1 Nov. 6
4.1 Measure Theory H16 H17 Nov. 6
4.2 Recurrence 4.2.3, H18 Nov. 13
4.5 Ergodic Theorems 4.5.1, 4.5.2, 4.5.5, 4.5.6 Nov. 13
4.3 Mixing 4.3.2, 4.3.3, 4.3.5, H19, 4.3.6, 4.3.7 Nov. 20
4.4 Examples 4.4 Nov. 20
4.6 Invariant measures 4.6.3, 4.6.4 4.6.5 Nov. 30
4.7 Unique Ergodicity 4.7.5, 4.7.6, 4.7.8, 4.7.9 Nov. 30