Shadowing Property in Systems with Singularities

Student: Zhevnerchuk Anton

Educational Programme: Mathematics (Bachelor)

Final Grade: 10

Year of Graduation: 2017

The tracing property in dynamical systems with singularities is studied. The tracing property means that for small perturbations the trajectories of the perturbed system are uniformly traced by the trajectories of the initial one. In the first part, we prove that if the phase space is an internally chain transitive set, then the system either has a classical tracing property, or almost any its pseudo-trajectory can not be approximated by a real one. In the second part, we give a definition of multiple tracing and discuss examples of systems with discontinuities satisfying this property.

Full text (added June 6, 2017)

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