BUT Faculty of Civil Engineering,

Department of Mathematics and Descriptive Geometry

invites you to a lecture

### Conditional Lipschitz shadowing for ordinary differential equations

**Tuesday 29th August 2023 at 13:00**

**Abstract.** We introduce the notion of conditional Lipschitz shadowing which does not aim to shadow every pseudo-orbit, but only those which belong to a certain prescribed set. We establish two types of sufficient conditions under which certain nonautonomous ordinary differential equations have such a property. The first criterion applies to a semilinear differential equation provided that its linear part is hyperbolic and the nonlinearity is small in a neighborhood of the prescribed set. The second criterion requires that the logarithmic norm of the derivative of the right-hand side with respect to the state variable is uniformly negative in a neighborhood of the prescribed set. The results are applicable to important classes of model equations including the logistic equation, whose conditional shadowing has recently been studied. Several examples are constructed showing that the obtained conditions are optimal.

**At the department meeting room (2 ^{nd} floor Z205), Žižkova 17.**

### THE LECTURE WILL BE GIVEN BY PROF. MIHÁLY PITUK,

*Department of Mathematics, University of Pannonia, Egyetem út 10, 8200, Veszprém, Hungary*

The lecture is intended for all those interested in these problems. It is supported by the programmes Excellence RP902315002 and PPSŘ RP122314001.

Ing. Jan Holešovský, Ph.D.

Head of the Institute of Mathematics and Descriptive Geometry