PreprintCC BY-NC-ND 4.0arXiv
A Hartman-Grobman theorem on Banach bundles
Abstract
We provide generalized linearization theorems for skew-product flows on abstract Banach bundles over locally compact metric spaces, allowing for a unified treatment of uniform and nonuniform, exponential and strong exponential dichotomies. This is accomplished by constructing an operator whose fixed points are exactly the conjugacies that are bounded perturbations of the identity, and by giving criteria under which this operator is a contraction. Under stronger assumptions we refine the argument to obtain Hölder regularity of the conjugacy. Finally, we apply our results to recover known results for non-autonomous differential equations and to obtain new linearization results for control-affine systems on manifolds.
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BibTeX
@misc{rogoll2026hartmangrobman,
title = {{A Hartman-Grobman theorem on Banach bundles}},
author = {Benjamin Rogoll and Stefan Siegmund},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40039},
eprint = {2609.40039},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40039},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - A Hartman-Grobman theorem on Banach bundles
AU - Benjamin Rogoll
AU - Stefan Siegmund
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40039
UR - https://arxiv.org/abs/2609.40039
AB - We provide generalized linearization theorems for skew-product flows on abstract Banach bundles over locally compact metric spaces, allowing for a unified treatment of uniform and nonuniform, exponential and strong exponential dichotomies. This is accomplished by constructing an operator whose fixed points are exactly the conjugacies that are bounded perturbations of the identity, and by giving criteria under which this operator is a contraction. Under stronger assumptions we refine the argument to obtain Hölder regularity of the conjugacy. Finally, we apply our results to recover known results for non-autonomous differential equations and to obtain new linearization results for control-affine systems on manifolds.
ER -