Event

# Integrability and limit cycles in polynomial systems of ODEs

• ### Thu 3 Feb 22

15:00 - 16:00

Zoom

• ### Event speaker

Valerij Romanovskij

• ### Event type

Lectures, talks and seminars
MESS

• ### Event organiser

Mathematical Sciences, Department of

• ### Contact details

Jesus Martinez-Garcia

These Departmental Seminars are for everyone in Maths. We encourage anyone interested in the subject in general, or in the particular subject of the seminar, to come along. It's a great opportunity to meet people in the Maths Department and join in with our community.

### Integrability and limit cycles in polynomial systems of ODEs

We discuss two problems related to the theory of  olynomial plane differential  systems,  that is, systems of the form:

$$\frac{dx}{dt}=P_{n}(x,y), \ \ \ \frac{dy}{dt}=Q_{n}(x,y),$$
where $P_{n}(x,y), Q_{n}(x,y)$ are polynomials of degree $n$, $x$ and $y$ are real unknown functions.

The first one  is the problem of local integrability, that is, the problem of  finding local analytic integrals in a neighborhood of singular points of system (1).  We present a computational approach to find integrable systems within given parametric families of systems and describe some mechanisms of integrability.

The second problem is called the cyclicity problem or the local 16th Hilbert problem and is related to the stimation of the number of limit cycles arising in system (1) after perturbations of integrable systems. The approach is algorithmic and is based on algorithms of computational commutative algebra relying on  the Groebner bases theory".

### Speaker

Valerij Romanovskij, University of Maribor

### How to attend

If not a member of the Dept. Mathematical Science at the University of Essex, you can register your interest in attending the seminar and request the Zoom’s meeting password by emailing Dr Jesus Martinez-Garcia (jesus.martinez-garcia@essex.ac.uk)