Skip to main content

ʗm-smoothness of invariant fiber bundles for dynamic equations on measure chains

Abstract

We present a new self-contained and rigorous proof of the smoothness of invariant fiber bundles for dynamic equations on measure chains or time scales. Here, an invariant fiber bundle is the generalization of an invariant manifold to the nonautonomous case. Our main result generalizes the “Hadamard-Perron theorem” to the time-dependent, infinite-dimensional, noninvertible, and parameter-dependent case, where the linear part is not necessarily hyperbolic with variable growth rates. As a key feature, our proof works without using complicated technical tools.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Christian Pötzsche.

Rights and permissions

This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.

About this article

Cite this article

Pötzsche, C., Siegmund, S. ʗm-smoothness of invariant fiber bundles for dynamic equations on measure chains. Adv Differ Equ 2004, 572930 (2004). https://doi.org/10.1155/S1687183904308010

Download citation

  • Received:

  • Published:

  • DOI: https://doi.org/10.1155/S1687183904308010