Complexity in Linear Systems: A Chaotic Linear Operator on the Space of Odd 2π-Periodic Functions
Not just nonlinear systems but infinite-dimensional linear systems can exhibit complex behavior. It has long been known that twice the backward shift on the space of square-summable sequences l2 displays chaotic dynamics. Here we construct the corresponding operator C on the space of 2π-periodic odd...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2017/6020213 |
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| _version_ | 1832548636776464384 |
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| author | Tamás Kalmár-Nagy Márton Kiss |
| author_facet | Tamás Kalmár-Nagy Márton Kiss |
| author_sort | Tamás Kalmár-Nagy |
| collection | DOAJ |
| description | Not just nonlinear systems but infinite-dimensional linear systems can exhibit complex behavior. It has long been known that twice the backward shift on the space of square-summable sequences l2 displays chaotic dynamics. Here we construct the corresponding operator C on the space of 2π-periodic odd functions and provide its representation involving a Principal Value Integral. We explicitly calculate the eigenfunction of this operator, as well as its periodic points. We also provide examples of chaotic and unbounded trajectories of C. |
| format | Article |
| id | doaj-art-c902d18e045641a29f85c4dd144bd4cb |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-c902d18e045641a29f85c4dd144bd4cb2025-02-03T06:13:36ZengWileyComplexity1076-27871099-05262017-01-01201710.1155/2017/60202136020213Complexity in Linear Systems: A Chaotic Linear Operator on the Space of Odd 2π-Periodic FunctionsTamás Kalmár-Nagy0Márton Kiss1Department of Fluid Mechanics, Faculty of Mechanical Engineering, Budapest University of Technology and Economics, Budapest, HungaryInstitute of Mathematics, Faculty of Natural Sciences, Budapest University of Technology and Economics, Budapest, HungaryNot just nonlinear systems but infinite-dimensional linear systems can exhibit complex behavior. It has long been known that twice the backward shift on the space of square-summable sequences l2 displays chaotic dynamics. Here we construct the corresponding operator C on the space of 2π-periodic odd functions and provide its representation involving a Principal Value Integral. We explicitly calculate the eigenfunction of this operator, as well as its periodic points. We also provide examples of chaotic and unbounded trajectories of C.http://dx.doi.org/10.1155/2017/6020213 |
| spellingShingle | Tamás Kalmár-Nagy Márton Kiss Complexity in Linear Systems: A Chaotic Linear Operator on the Space of Odd 2π-Periodic Functions Complexity |
| title | Complexity in Linear Systems: A Chaotic Linear Operator on the Space of Odd 2π-Periodic Functions |
| title_full | Complexity in Linear Systems: A Chaotic Linear Operator on the Space of Odd 2π-Periodic Functions |
| title_fullStr | Complexity in Linear Systems: A Chaotic Linear Operator on the Space of Odd 2π-Periodic Functions |
| title_full_unstemmed | Complexity in Linear Systems: A Chaotic Linear Operator on the Space of Odd 2π-Periodic Functions |
| title_short | Complexity in Linear Systems: A Chaotic Linear Operator on the Space of Odd 2π-Periodic Functions |
| title_sort | complexity in linear systems a chaotic linear operator on the space of odd 2π periodic functions |
| url | http://dx.doi.org/10.1155/2017/6020213 |
| work_keys_str_mv | AT tamaskalmarnagy complexityinlinearsystemsachaoticlinearoperatoronthespaceofodd2pperiodicfunctions AT martonkiss complexityinlinearsystemsachaoticlinearoperatoronthespaceofodd2pperiodicfunctions |