- #1
logarithmic
- 107
- 0
Homework Statement
This is from Henle's Combinatorial Introduction to Topology, section 9 question 2d).
Here's the phase portrait: http://img69.imageshack.us/img69/70/phasepor.jpg
Find the index of the point in the center of that picture.
The Attempt at a Solution
I used the fact that index = 1 + (e - h)/2, where e = number of elliptic sectors, and h = number of hyperbolic sectors.
In the picture, only D is elliptic, so e = 1, and B, E, F are hyperbolic, so h = 3, which gives index = 0. (A and C are parabolic sectors and don't count for the purposes of finding the index.)
The correct answer is -2. Which can be confirmed by noting that if we pick "pointing upwards" as a reference direction, only at X and Y does it point upwards, and at both these places there is a clockwise turn (a turn in the negative direction), so index = -2.
What's wrong with the first method?
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