Browsing by Author "Perić, Milan"
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Perić, Milan (Beograd , 2021)[more][less]
Abstract: This thesis presents a method for calculating the polynomial entropy of the topolog- ical dynamic system with finitely many non-wandering points. A special coding is adapted for such systems. Thanks to this coding the polynomial entropy can be bounded by the number of specific mutually singular points in the closures of stable manifolds of non-wandering points. This method was applied to Morse gradient systems. It is shown that the polynomial entropy of the Morse gradient system is bounded by n(F ) − 1, where n(F ) is the number of different Morse indices of critical points of the Morse function F. If Morse gradient systems on mani- folds of dimension n has only critical points of indices 0 and n, it is proved that the polynomial entropy is equal to 1, and if the system has critical points of indices 0, n/2 and n, it is proved that polynomial entropy is equal to 2. The polynomial entropy for different parameter values in logistic map has also been calculated, and it has been shown that the polynomial entropy distinguishes the systems of low complexity with drastically different behaviours, which cannot be distinguished by the topological entropy. The example of the homeomorphism of the con- nected compact metric space that is not equicontinuous and with vanishing polynomial entropy is also given. URI: http://hdl.handle.net/123456789/5800 Files in this item: 1
Disertacija_12349.pdf ( 731.8Kb ) -
Perić, Milan (Beograd , 2021)[more][less]
Abstract: his thesis presents a method for calculating the polynomial entropy of the topolog-ical dynamic system with finitely many non-wandering points. A special coding is adapted forsuch systems. Thanks to this coding the polynomial entropy can be bounded by the numberof specific mutually singular points in the closures of stable manifolds of non-wandering points.This method was applied to Morse gradient systems. It is shown that the polynomial entropyof the Morse gradient system is bounded byn(F) URI: http://hdl.handle.net/123456789/5215 Files in this item: 1
Milan_Peric_disertacija.pdf ( 731.8Kb ) -
Perić, Milan (Beograd , 2020)[more][less]
URI: http://hdl.handle.net/123456789/4903 Files in this item: 1
Simplektomorfizmi i fluks-hipoteza.pdf ( 470.7Kb )
Now showing items 1-3 of 3