Hilbert’s 16-th problem solved. Or not?..

Hilbert’s 16th problem. When variational principles meet differential systems

Jaume Llibre, Pablo Pedregal

We provide an upper bound for the number of limit cycles that polynomial differential systems of a given degree may have. The bound turns out to be a polynomial of degree four in the degree of the system. Under suitable conditions the technique is applicable to general smooth differential systems as well. It brings together those two areas of Analysis implied in the title, by transforming the task of counting limit cycles into counting critical points for a certain smooth, non-negative functional for which limit cycles are zeroes. We thus solve the second part of Hilbert’s 16th problem providing a uniform upper bound for the number of limit cycles which only depends on the degree of the polynomial differential system.

Link to arXiv


About Artem Novozhilov

I am an applied mathematician interested in studying various evolutionary processes by means of mathematical models. More on my professional activities can be found on my page https://www.ndsu.edu/pubweb/~novozhil/
This entry was posted in Math 266: Intro to ODE, News and tagged . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s