Attractors of Strongly Dissipative Systems

A. G. Ramm. "Attractors of Strongly Dissipative Systems." Bulletin of the Polish Academy of Sciences. Mathematics 57.1 (2009): 25-31. <http://eudml.org/doc/281191>.

@article{A2009,
abstract = {A class of infinite-dimensional dissipative dynamical systems is defined for which there exists a unique equilibrium point, and the rate of convergence to this point of the trajectories of a dynamical system from the above class is exponential. All the trajectories of the system converge to this point as t → +∞, no matter what the initial conditions are. This class consists of strongly dissipative systems. An example of such systems is provided by passive systems in network theory (see, e.g., MR0601947 (83m:45002)).},
author = {A. G. Ramm},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {dissipative systems; dynamical systems; attractors; invariant manifolds; nonlinear evolution},
language = {eng},
number = {1},
pages = {25-31},
title = {Attractors of Strongly Dissipative Systems},
url = {http://eudml.org/doc/281191},
volume = {57},
year = {2009},
}

TY - JOUR
AU - A. G. Ramm
TI - Attractors of Strongly Dissipative Systems
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2009
VL - 57
IS - 1
SP - 25
EP - 31
AB - A class of infinite-dimensional dissipative dynamical systems is defined for which there exists a unique equilibrium point, and the rate of convergence to this point of the trajectories of a dynamical system from the above class is exponential. All the trajectories of the system converge to this point as t → +∞, no matter what the initial conditions are. This class consists of strongly dissipative systems. An example of such systems is provided by passive systems in network theory (see, e.g., MR0601947 (83m:45002)).
LA - eng
KW - dissipative systems; dynamical systems; attractors; invariant manifolds; nonlinear evolution
UR - http://eudml.org/doc/281191
ER -