Qualitative properties of impulsive semidynamical systems

• Ano de defesa: 2017
• Autor(a) principal: Souto, Ginnara Mexia
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Dissipatividade; Dissipativity; Dynamical systems; Estabilidade; Impulses; Impulsos; Recorrência; Recurrence; Sistemas dinâmicos; Stability
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-18042017-110611/

The theory of impulsive dynamical systems is an important tool to describe the evolution of systems where the continuous development of a process is interrupted by abrupt changes of state. This phenomenon is called impulse. In many natural phenomena, the real deterministic models are often described by systems which involve impulses. The aim of this work is to investigate topological properties of impulsive semidynamical systems. We establish necessary and sufficient conditions to obtain uniform and orbital stability via Lyapunov functions. We solve a problem of Jake Hale for impulsive systems where we obtain the existence of a maximal compact invariant set. Also, we obtain results about almost periodic motions and asymptotically almost periodic motions in the context of impulsive systems. Some asymptotic properties for impulsive systems and for their associated discrete systems are investigated. The new results presented in this text are in the papers [11], [15] and [16].