- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:24
Portugaliae Mathematica
Port. Math.
PM
0032-5155
1662-2758
General
10.4171/PM
http://www.ems-ph.org/doi/10.4171/PM
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2008)
73
2016
1
Nonuniform dichotomic behavior: Lipschitz invariant manifolds for difference equations
António
Bento
Universidade da Beira Interior, COVILHÃ, PORTUGAL
César
Silva
Universidade da Beira Interior, COVILHÃ, PORTUGAL
Invariant manifolds, nonautonomous difference equations, nonuniform dichotomies
We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear difference equations assuming a very general form of dichotomic behavior for the linear equation. The results are obtained using Banach fixed point theorem and include situations where the behavior is far from hyperbolic. We also give several new examples and show that our result includes as particular cases several previous theorems.
Dynamical systems and ergodic theory
Ordinary differential equations
41
64
10.4171/PM/1975
http://www.ems-ph.org/doi/10.4171/PM/1975