We have investigated the relationship between the sensitivity of linear dynamical systems on separable Banach spaces and F-sensitivity for its induced hyperspace dynamics, and we have solved the following problems.
We have found a relation between F-sensitivity derived from the linear dynamical system (X,T) and thereby the hyperspace K(X) of compact subsets and the hyperspace C(X) of compact convex subsets.
We have obtained new results by using the dynamic approach by Hausdorff distance on hyperspace, showing that the sensitivity of the bounded linear operators on separable Banach spaces and by them the genetic family of systems induced in hyperspace of compact and compact convex sets is equivalent.
We also support examples of our results.
Our results can be used to mathematically model the linear chaos phenomenon of a magnetostatic oscillator without external forces, modeled by the Schrodinger equation, in a laser in the optical or infrared region.
The result was published in "ACTA MATHEMATICA SINICA-ENGLISH SERIES" under the title of "F-sensitivity for linear dynamics and its induced hyperspace dynamics"
