On Jack Hale's problem for impulsive systems

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Author(s):	Bonotto, E. M. ^[1] ; Gimenes, L. P. ^[2] ; Souto, G. M. ^[1] Total Authors: 3
Affiliation:	^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil ^[2] Univ Estadual Maringa, BR-87020900 Maringa, Parana - Brazil Total Affiliations: 2
Document type:	Journal article
Source:	Journal of Differential Equations; v. 259, n. 2, p. 642-665, JUL 15 2015.
Web of Science Citations:	4
Abstract
An interesting problem of Jack Hale deals with the existence of a maximal compact invariant set in discrete dynamical systems. A solution for this problem is known for locally bounded dynamical systems. Following this line of research, we consider in this paper a class of systems whose continuous dynamics are interrupted by abrupt changes of state and we present sufficient conditions to obtain the existence of a maximal compact invariant set for a system in this class. We use the theory of asymptotic compactness to get the results. (C) 2015 Elsevier Inc. All rights reserved. (AU)

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


FAPESP's process:	12/16709-6 - Non-autonomous systems with impulses: convergent systems and the Navier-Stokes Equation
Grantee:	Everaldo de Mello Bonotto
Support Opportunities:	Regular Research Grants