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arXiv · 2307.15102

Best Ulam constants for two-dimensional non-autonomous linear differential systems

Douglas R. Anderson·Masakazu Onitsuka·Donal O'Regan
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Abstract

This study deals with the Ulam stability of non-autonomous linear differential systems without assuming the condition that they admit an exponential dichotomy. In particular, the best (minimal) Ulam constants for two-dimensional non-autonomous linear differential systems with generalized Jordan normal forms are derived. The obtained results are applicable not only to systems with solutions that exist globally on $(-\infty,\infty)$, but also to systems with solutions that blow up in finite time. New results are included even for constant coefficients. A wealth of examples are presented, and approximations of node, saddle, and focus are proposed. In addition, this is the first study to derive the best Ulam constants for non-autonomous systems other than periodic systems.

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Douglas R. Anderson, Masakazu Onitsuka, Donal O'Regan. 2023-07-27. Best Ulam constants for two-dimensional non-autonomous linear differential systems. https://arxiv.org/abs/2307.15102

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