Parametric topological entropy and differential equations with time–dependent impulses II: Multivalued case.

The main aim of this article is to establish an effective criterion for a positive parametric topological entropy to differential equations with multivalued nonautonomous impulses on tori. The crucial tool for this goal consists in developing an appropriate Ivanov-like inequality for the lower estimate of a new kind of entropy by means of the logarithm of asymptotic Nielsen numbers for the compositions of a one-parameter family of multivalued admissible maps. This inequality is then applied to impulsive differential equations on tori via the associated Poincaré translation operators along their trajectories. The obtained results generalize in a significant way those in our recent papers, especially in the one with the same title (whence the indication by II), into a multivalued setting. Another nontrivial generalization can be regarded with respect to their simple reduction into a "nonparametric" case. [ABSTRACT FROM AUTHOR]