Topics for Final, Math 313- 2, June 2003
The questions of the
Test from 2002 are all reasonable.
Also, question 5 from Final 313-1 in
2002.
The following topics were covere before the midterm:
problems relating to each topic from previous tests are given.
- Invariant measures and frequency measures:
Sections 4.4.1, 4.4.2, 4.4.3
- HW 4.4.1, 4.4.2, 4.4.3
- problems 5 , Final 313-1, 2002
- Linear Maps: Section 5.1
- HW 5.5.1
- problem 1, Test 2002
- Stability of periodic points: Sections 5.2,
- HW 5.2.3, 5.2.6
- problem 2, Test 2002; problem 5, final 2002;
problems 4 & 5, final 1998; problem 3, final 1995
- Stable manifolds: Section 5.3
- HW 5.3.1
- problem 3, Test 2002
- Geometric horseshoe: Section 6.1.
- HW 6.1.1, 6.1.3
- problem 5, Test 2002
- Symbolic dynamics (correctly aligned boxes, Markov partitions):
Section 6.2.1 & 6.2.2 (latest version).
- HW 6.2.1 & 6.2.2 (6.3.1 as originally assigned)
- problem 4, Test 2002; problem 4, final 2002; problem 1, final 1998;
problem 2(a,b) (essential = nonzero index), final 1995
- Attractors: Section 6.4: used as examples for Markov
partitions
The following topics were covere after the midterm:
problems relating to each topic from previous tests are given.
- Homoclinic points: Section 6.3:
- HW 6.3.1 (about heteroclinic point, some versions of HW were
numbered differently)
- Attractors: Section 6.4:
- HW 6.4.4 (modified solenoid)
- problem 6, Final 2002
- Lyapunov exponents: Sections 6.5, 6.5.1, 6.5.2:
- HW 6.5.2, 6.5.3
- problem 3, final 2002; problem 4(a,b), final 1999;
problem 2c, final 1995
- Box dimension: Section 7.1 :
- HW 7.1.1, 7.1.2, 7.1.6, 7.1.7
- problem 2c, final 2002; problem 1, final 2002;
problem 5b, final 1999; problem 5b, final 1995
- Iterated Function Systems: Section 7.3, 7.3.1, 7.3.2, 7.3.3
:
- HW 7.3.1, 7.3.3, 7.3.6
- problem 2, final 2002; problem 5a, final 1999;
problem 5(a,d), final 1995