Comments on: Shilnikov’s theorems on bifurcation from a homoclinic orbit http://alanrendall.wordpress.com/2009/03/26/shilnikovs-theorems-on-bifurcation-from-a-homoclinic-orbit/ A mathematician thinks aloud Thu, 09 May 2013 07:10:22 +0000 hourly 1 http://wordpress.com/ By: Michele Berra http://alanrendall.wordpress.com/2009/03/26/shilnikovs-theorems-on-bifurcation-from-a-homoclinic-orbit/#comment-371 Sat, 05 Jun 2010 08:36:41 +0000 http://alanrendall.wordpress.com/?p=461#comment-371 Hi Alan,

Thank for the advice, i will take a look on this book.

Regards,

Michele

]]> By: hydrobates http://alanrendall.wordpress.com/2009/03/26/shilnikovs-theorems-on-bifurcation-from-a-homoclinic-orbit/#comment-370 Wed, 02 Jun 2010 17:06:26 +0000 http://alanrendall.wordpress.com/?p=461#comment-370 Hi,

The book of Kuznetsov which I quoted in my post is the best I have found about this subject. In fact I am not an expert in this area but rather someone who is gradually getting into the subject,

Regards,
Alan

]]> By: Michele Berra http://alanrendall.wordpress.com/2009/03/26/shilnikovs-theorems-on-bifurcation-from-a-homoclinic-orbit/#comment-369 Wed, 02 Jun 2010 14:41:14 +0000 http://alanrendall.wordpress.com/?p=461#comment-369 Your post look interesting. I’m a student of mathematics and i’m only a beginner on bifurcations. I have planned to study a system in which a periodic orbits bifurcates from a homoclinic loop. Have you got some references or suggestions for my research?

Regards,

Michele Berra

]]> By: Hopf bifurcations and Lyapunov numbers « Hydrobates http://alanrendall.wordpress.com/2009/03/26/shilnikovs-theorems-on-bifurcation-from-a-homoclinic-orbit/#comment-296 Sun, 10 Jan 2010 13:14:47 +0000 http://alanrendall.wordpress.com/?p=461#comment-296 [...] My primary source of information on this subject is the book of Kuznetsov already mentioned in a previous post. The figures 3.5 and 3.7 of that book are useful for visualizing what is going on. If a further [...]

]]> By: hydrobates http://alanrendall.wordpress.com/2009/03/26/shilnikovs-theorems-on-bifurcation-from-a-homoclinic-orbit/#comment-122 Fri, 27 Mar 2009 10:30:31 +0000 http://alanrendall.wordpress.com/?p=461#comment-122 My statements about type I and type II critical collapse in the original version of this post were not correct and I have now fixed this. I thank Piotr Bizon for drawing my attention to this.

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