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math.DS2021
Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps
Sergey Kryzhevich, Viktor Avrutin, Nikita Begun +2
We studied topological and metric properties of the so-called interval translation maps (ITMs). For these maps, we introduced the maximal invariant measure and study its properties…
math.DS2017
Chaos in Saw Map
Nikita Begun, Pavel Kravetc, Dmitrii Rachinskii
We consider dynamics of a scalar piecewise linear "saw map" with infinitely many linear segments. In particular, such maps are generated as a Poincaré map of simple two-dimensional…
math.DS2016
Dynamics of Discrete Time Systems with a Hysteresis Stop Operator
Maxim Arnold, Nikita Begun, Pavel Gurevich +3
We consider a piecewise linear two-dimensional dynamical system that couples a linear equation with the so-called stop operator. Global dynamics and bifurcations of this system are…