Entropy of Impulsive Semi-flow on Subsets

Based on the theory of Carathéodory structure, this paper introduces several definitions of entropies for impulsive semi-flows on arbitrary subsets. We compare these definitions and establish relations of these definitions. We show an inverse variational principle between topological \(\tau \) $\tau$ -entropy and measure theoretic \(\tau \) $\tau$ -entropy. Moreover, a variational principle of packing \(\tau \) $\tau$ entropy of impulsive semi-flows is established.