Reduction principle at work
The purpose of this informal paper is three-fold: First, filling a gap in the literature, we provide a (necessary and sufficient) principle of linearized stability for nonautonomous difference equations in Banach spaces based on the dichotomy spectrum. Second, complementing the above, we survey and...
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De Gruyter
2021
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oai:doaj.org-article:f8ad6839777a4e7cb5976838422ca34b2021-12-05T14:10:56ZReduction principle at work2353-062610.1515/msds-2020-0124https://doaj.org/article/f8ad6839777a4e7cb5976838422ca34b2021-04-01T00:00:00Zhttps://doi.org/10.1515/msds-2020-0124https://doaj.org/toc/2353-0626The purpose of this informal paper is three-fold: First, filling a gap in the literature, we provide a (necessary and sufficient) principle of linearized stability for nonautonomous difference equations in Banach spaces based on the dichotomy spectrum. Second, complementing the above, we survey and exemplify an ambient nonautonomous and infinite-dimensional center manifold reduction, that is Pliss’s reduction principle suitable for critical stability situations. Third, these results are applied to integrodifference equations of Hammerstein- and Urysohn-type both in C- and Lp-spaces. Specific features of the nonautonomous case are underlined. Yet, for the simpler situation of periodic time-dependence even explicit computations are feasible.Pötzsche ChristianRuss EvamariaDe Gruyterarticlenonautonomous difference equationperiodic difference equationlinearized stabilitydichotomy spectrumcenter manifold reductionintegrodifference equation39a3037c60MathematicsQA1-939ENNonautonomous Dynamical Systems, Vol 8, Iss 1, Pp 46-74 (2021) |
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DOAJ |
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DOAJ |
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EN |
| topic |
nonautonomous difference equation periodic difference equation linearized stability dichotomy spectrum center manifold reduction integrodifference equation 39a30 37c60 Mathematics QA1-939 |
| spellingShingle |
nonautonomous difference equation periodic difference equation linearized stability dichotomy spectrum center manifold reduction integrodifference equation 39a30 37c60 Mathematics QA1-939 Pötzsche Christian Russ Evamaria Reduction principle at work |
| description |
The purpose of this informal paper is three-fold: First, filling a gap in the literature, we provide a (necessary and sufficient) principle of linearized stability for nonautonomous difference equations in Banach spaces based on the dichotomy spectrum. Second, complementing the above, we survey and exemplify an ambient nonautonomous and infinite-dimensional center manifold reduction, that is Pliss’s reduction principle suitable for critical stability situations. Third, these results are applied to integrodifference equations of Hammerstein- and Urysohn-type both in C- and Lp-spaces. Specific features of the nonautonomous case are underlined. Yet, for the simpler situation of periodic time-dependence even explicit computations are feasible. |
| format |
article |
| author |
Pötzsche Christian Russ Evamaria |
| author_facet |
Pötzsche Christian Russ Evamaria |
| author_sort |
Pötzsche Christian |
| title |
Reduction principle at work |
| title_short |
Reduction principle at work |
| title_full |
Reduction principle at work |
| title_fullStr |
Reduction principle at work |
| title_full_unstemmed |
Reduction principle at work |
| title_sort |
reduction principle at work |
| publisher |
De Gruyter |
| publishDate |
2021 |
| url |
https://doaj.org/article/f8ad6839777a4e7cb5976838422ca34b |
| work_keys_str_mv |
AT potzschechristian reductionprincipleatwork AT russevamaria reductionprincipleatwork |
| _version_ |
1718371578987675648 |