Robert Szczelina

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math.DS2024

Sharkovskii theorem for infinite dimensional dynamical systems

Anna Gierzkiewicz, Robert Szczelina

We present an adaptation of a relatively simple topological argument to show the existence of many periodic orbits in an infinite dimensional dynamical system, provided that the sy…

math.DS2024

Stable periodic orbits for delay differential equations with unimodal feedback

Gábor Benedek, Tibor Krisztin, Robert Szczelina

We consider delay differential equations of the form $y^{'} (t) = - a y (t) + b f (y (t - 1))$ with positive parameters $a, b$ and a unimodal $f : [0, \infty) \to [0, 1]$ . It is assumed that the nonli…