Naslov
Conditional Lipschitz shadowing for ordinary differential equations

Autori
Backes, Lucas ; Dragičević, Davor ; Onitsuka, Masakazu ; Pituk, Mihaly

Vrsta, podvrsta
Radovi u časopisima, znanstveni

Izvornik
Journal of dynamics and differential equations (2023)

Status rada
Prihvaćen

Ključne riječi
shadowing, Hyers--Ulam stability, exponential dichotomy, logarithmic norm

Sažetak
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 non\- auto\-nomous 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA