The deterministic chaos in the sense of a positive topological entropy is investigated for differential equations with multivalued impulses. Two definitions of topological entropy are examined for three classes of multivalued maps: n-valued maps, Rδ-maps and admissible maps in the sense of Górniewicz. The principal tool for its lower estimates and, in particular, its positivity are the Ivanov-type inequalities in terms of the asymptotic Nielsen numbers. The obtained results are then applied to impulsive differential equations via the associated Poincaré translation operators along their trajectories. The main theorems for chaotic differential equations with multivalued impulses are formulated separately on compact subsets of Euclidean spaces and on tori. Several illustrative examples are supplied.

中文翻译：

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多值脉冲微分方程的混沌

研究了具有多值脉冲的微分方程在正拓扑熵意义上的确定性混沌。针对三类多值映射检查拓扑熵的两个定义：n值的地图，Rδ-Górniewicz 意义上的地图和可接受的地图。其较低估计的主要工具，特别是其积极性是渐近尼尔森数方面的伊万诺夫型不等式。然后通过相关的庞加莱平移算子沿其轨迹将获得的结果应用于脉冲微分方程。具有多值冲量的混沌微分方程的主要定理分别在欧几里得空间的紧子集和环面上制定。提供了几个说明性示例。