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A uniform exponential spectrum for linear flows on vector bundles

Title data

Grüne, Lars:
A uniform exponential spectrum for linear flows on vector bundles.
In: Journal of Dynamics and Differential Equations. Vol. 12 (March 2000) Issue 2 . - pp. 435-448.
ISSN 1572-9222
DOI: https://doi.org/10.1023/A:1009024610394

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Abstract in another language

For a linear flow on a vector bundle we define a uniform exponential spectrum. For a compact invariant set for the projected flow we obtain this spectrum by taking all accumulation points for the time tending to infinity of the union over the finite time exponential growth rates for all initial values in this set. Using direct arguments we show that for a connected compact invariant set this spectrum is a closed interval whose boundary points are Lyapunov exponents. For a compact invariant set on which the flow is chain transitive we show that this spectrum coincides with the Morse spectrum. In particular this approach admits a straightforward analytic proof for the regularity and continuity properties of the Morse spectrum without using cohomology or ergodicity results.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: linear flow; uniform; exponential spectrum; Lyapunov exponent; accumulation point
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 22 Feb 2021 08:26
Last Modified: 07 May 2021 06:43
URI: https://eref.uni-bayreuth.de/id/eprint/63257