Abstract
Invariant fiber bundles are the generalization of invariant manifolds from discrete dynamical systems (mappings) to non-autonomous difference equations. In this paper we present a self-contained proof of their existence and smoothness. Our main result generalizes the so-called “Hadamard–Perron-Theorem” for time-dependent families of pseudo-hyperbolic mappings from the finite-dimensional invertible to the infinite-dimensional non-invertible case.
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Aulbach, B., Pötzsche, C. & Siegmund, S. A Smoothness Theorem for Invariant Fiber Bundles. Journal of Dynamics and Differential Equations 14, 519–547 (2002). https://doi.org/10.1023/A:1016383031231
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DOI: https://doi.org/10.1023/A:1016383031231