Comments on: Lyapunov-Schmidt reduction http://alanrendall.wordpress.com/2008/12/07/lyapunov-schmidt-reduction/ A mathematician thinks aloud Thu, 09 May 2013 07:10:22 +0000 hourly 1 http://wordpress.com/ By: hydrobates http://alanrendall.wordpress.com/2008/12/07/lyapunov-schmidt-reduction/#comment-524 Wed, 02 Feb 2011 15:26:09 +0000 http://alanrendall.wordpress.com/?p=196#comment-524 Hi,

What I wrote is not wrong but I have been a little sloppy with the notation. I said ‘do linear transformations independently in the domain and range’ which implies that I am using two different bases. However I did not choose different notations for them. It would have been more precise (and less confusing?) if I had put primes on the basis vectors with indices 2 to n.

]]> By: Grigory Bordyugov http://alanrendall.wordpress.com/2008/12/07/lyapunov-schmidt-reduction/#comment-523 Wed, 02 Feb 2011 13:55:49 +0000 http://alanrendall.wordpress.com/?p=196#comment-523 A terrific read, thanks! I was trying to understand the LS reduction and found your explanation excellent.

Just one more technical remark: in general, I guess, the range and the nullspace of N are not complimentary (this is true however if N^2 = N, i.e. N is a kind of projections). That would mean that if e_1 spans the nullspace, that wouldn’t automatically imply that e_2, …, e_n span the whole range. But I guess you’re interested just in e_1 anyway. Please correct me if I’m wrong.

Yours.

]]> By: hydrobates http://alanrendall.wordpress.com/2008/12/07/lyapunov-schmidt-reduction/#comment-121 Fri, 27 Mar 2009 09:44:36 +0000 http://alanrendall.wordpress.com/?p=196#comment-121 I have corrected some typos in the original post. I thank Roger Bieli for pointing them out to me.

]]> By: Shilnikov’s theorems on bifurcation from a homoclinic orbit « Hydrobates http://alanrendall.wordpress.com/2008/12/07/lyapunov-schmidt-reduction/#comment-120 Thu, 26 Mar 2009 10:32:41 +0000 http://alanrendall.wordpress.com/?p=196#comment-120 [...] is it must be infinite-dimensional. In the most optimistic case some kind of centre manifold or Lyapunov-Schmidt reduction might be used to get back to a finite-dimensional (even low-dimensional) system. Another problem, [...]

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