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Quasigauge spaces with generalized quasipseudodistances and periodic points of dissipative set-valued dynamic systems. (English) Zbl 1213.81161
The authors introduce the families of generalized quasipseudodistances in quasigauge spaces and define three kinds of dissipative set-valued dynamic systems with these families of generalized quasi-pseudodistances and with some families of not necessarily lower semicontinuous entropies. Assuming that quasigauge spaces are left $K$ sequentially complete (but not necessarily Hausdorff), they prove that for each starting point each dynamic process or generalized sequence of iterations of these dissipative set-valued dynamic systems left converges. They also show that if an iterate of these dissipative set-valued dynamic systems is left quasiclosed, then these limit points are periodic points. Examples illustrating ideas, methods, definitions, and results are constructed.

##### MSC:
 81S22 Open systems, reduced dynamics, master equations, decoherence (quantum theory) 37L99 Infinite-dimensional dissipative dynamical systems
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