Topological Methods in Nonlinear Analysis

Analytic invariant manifolds for nonautonomous equations

Luis Barreira and Claudia Valls

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We construct real analytic stable invariant manifolds for sufficiently small perturbations of a linear equation $v'=A(t)v$ admitting a nonuniform exponential dichotomy. As a byproduct of our approach we obtain an exponential control not only of the trajectories on the invariant manifolds, but also of all their derivatives.

Article information

Topol. Methods Nonlinear Anal., Volume 46, Number 1 (2015), 29-43.

First available in Project Euclid: 30 March 2016

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Barreira, Luis; Valls, Claudia. Analytic invariant manifolds for nonautonomous equations. Topol. Methods Nonlinear Anal. 46 (2015), no. 1, 29--43. doi:10.12775/TMNA.2015.035.

Export citation


  • L. Barreira and Ya. Pesin, Nonuniform Hyperbolicity, Encyclopedia Math. Appl. 115, Cambridge Univ. Press, 2007.
  • L. Barreira and C. Valls, Analytic invariant manifolds for sequences of diffeomorphisms, J. Differential Equations 245 (2008), 80–101.
  • E. Bedford, M. Lyubich and J. Smillie, Polynomial diffeomorphisms of $\C^2$. \romIV: the measure of maximal entropy and laminar currents, Invent. Math. 112 (1993), 77–125.
  • E. Bedford and J. Smillie, Polynomial diffeomorphisms of $\C^2:$ currents, equilibrium measure and hyperbolicity, Invent. Math. 103 (1991), 69–99.
  • M. Jonsson and D. Varolin, Stable manifolds of holomorphic diffeomorphisms, Invent. Math. 149 (2002), 409–430.
  • Ya. Pesin, Families of invariant manifolds corresponding to nonzero characteristic exponents, Math. USSR Izv. 10 (1976), 1261–1305.
  • H. Wu, Complex stable manifolds of holomorphic diffeomorphisms, Indiana Univ. Math. J. 42 (1993), 1349–1358.