Cds202-hw3_wi09

Cds202-hw3_wi09 - n ) is a matrix of dimension n ( n 1) / 2...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
CALIFORNIA INSTITUTE OF TECHNOLOGY Control and Dynamical Systems CDS 202 R. Murray Winter 2009 Problem Set #3 Issued: 22 Jan 09 Due: 29 Jan 09 Reading: Abraham, Marsden, and Ratiu (MTA), sections 2.5 and 3.5 Problems: 1. MTA 2.5-3 (i), (ii) and (iv): exponential maps. You can assume (iii), which is a bit tricky to prove. 2. MTA 2.5-4: Equivalence of implicit and inverse function theorems. 3. MTA 2.5-12: Roots of polynomials are smooth functions of polynomial coe±cients. 4. MTA 3.5-1 (i)–(ii): matrix manifolds. For (ii), you focus on showing that O (
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: n ) is a matrix of dimension n ( n 1) / 2 (you already showed it has two components in HW #1). 5. [Guillemin and Pollack, page 18, #6; MTA 3.5-5] (a) If f and g are submersions/immersions, show that f g is. (b) If f and g are submersions/immersions, show that g f is. (c) If f is an immersion, show that its restriction to any submanifold of its domain is an immersion. (d) When dim M = dim N , show that submersions/immersions f : M N are the same as local dieomorphisms. 6. MTA 3.5-11: covering maps....
View Full Document

Ask a homework question - tutors are online