Qualitative properties of impulsive semidynamical systems

Author(s)

Ginnara Mexia Souto

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2017-02-06

Examining board members

Everaldo de Mello Bonotto; Andréa Cristina Prokopczyk Arita; Marcelo Rempel Ebert; Ma To Fu; Tomás Caraballo Garrido

• Advisor: Everaldo de Mello Bonotto; Márcia Cristina Anderson Braz Federson

Abstract

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]. (AU)

• FAPESP's process: 12/20933-9 - Qualitative properties of impulsive semidynmical systems
• Grantee: Ginnara Mexia Souto
• Support Opportunities: Scholarships in Brazil - Doctorate