TY - JOUR
T1 - Fixed set iterations for relaxed Lipschitz multimaps
AU - Donchev, Tzanko
AU - Farkhi, Elza
AU - Reich, Simeon
N1 - Funding Information:
The third author was partially supported by the Fund for the Promotion of Research at the Technion and by the Technion VPR Fund.
PY - 2003/6
Y1 - 2003/6
N2 - A dynamical system described by an autonomous differential inclusion with a right-hand side satisfying a relaxed Lipschitz condition, as well as its Euler approximations, are studied. We investigate the asymptotic properties of the solutions and of the attainable sets. It is shown that the system has a strongly flow invariant set, or a "fixed set", that is, a set such that each trajectory starting from it does not leave it. This set is also an attractor, i.e., it attracts the continuous and the discrete Euler trajectories as the time tends to infinity. We give estimates of the rate of attraction. An algorithm for approximating the fixed set by the attainable sets of the discrete system is also presented.
AB - A dynamical system described by an autonomous differential inclusion with a right-hand side satisfying a relaxed Lipschitz condition, as well as its Euler approximations, are studied. We investigate the asymptotic properties of the solutions and of the attainable sets. It is shown that the system has a strongly flow invariant set, or a "fixed set", that is, a set such that each trajectory starting from it does not leave it. This set is also an attractor, i.e., it attracts the continuous and the discrete Euler trajectories as the time tends to infinity. We give estimates of the rate of attraction. An algorithm for approximating the fixed set by the attainable sets of the discrete system is also presented.
KW - Attractor
KW - Differential inclusion
KW - Fixed point
KW - Flow invariant set
KW - One-sided Lipschitz condition
KW - Relaxed Lipschitz condition
UR - http://www.scopus.com/inward/record.url?scp=0037410110&partnerID=8YFLogxK
U2 - 10.1016/S0362-546X(03)00036-1
DO - 10.1016/S0362-546X(03)00036-1
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AN - SCOPUS:0037410110
SN - 0362-546X
VL - 53
SP - 997
EP - 1015
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 7-8
ER -