## Topological Methods in Nonlinear Analysis

### Analytic invariant manifolds for nonautonomous equations

#### Abstract

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

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

Dates
First available in Project Euclid: 30 March 2016

https://projecteuclid.org/euclid.tmna/1459343883

Digital Object Identifier
doi:10.12775/TMNA.2015.035

Mathematical Reviews number (MathSciNet)
MR3443676

Zentralblatt MATH identifier
1364.37068

#### Citation

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. https://projecteuclid.org/euclid.tmna/1459343883

#### References

• 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.