Periodic solutions of arbitrary length in a simple integer iteration
<p/> <p>We prove that all solutions to the nonlinear second-order difference equation in integers <it>y</it><sub><it>n</it>+1</sub> = ⌈<it>ay</it><sub><it>n</it></sub>⌉-<it>y</it><s...
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SpringerOpen
2006-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://www.advancesindifferenceequations.com/content/2006/035847 |
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doaj-dcf2aa8342a04a2eb071ad6555e7f2202020-11-25T00:15:22ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472006-01-0120061035847Periodic solutions of arbitrary length in a simple integer iterationClark Dean<p/> <p>We prove that all solutions to the nonlinear second-order difference equation in integers <it>y</it><sub><it>n</it>+1</sub> = ⌈<it>ay</it><sub><it>n</it></sub>⌉-<it>y</it><sub><it>n</it>-1</sub>, {<it>a</it> ∈ ℝ:|<it>a</it>|<2, <it>a</it>≠0,±1}, <it>y</it><sub>0</sub>, <it>y</it><sub>1</sub> ∈ ℤ, are periodic. The first-order system representation of this equation is shown to have self-similar and chaotic solutions in the integer plane.</p> http://www.advancesindifferenceequations.com/content/2006/035847 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Clark Dean |
| spellingShingle |
Clark Dean Periodic solutions of arbitrary length in a simple integer iteration Advances in Difference Equations |
| author_facet |
Clark Dean |
| author_sort |
Clark Dean |
| title |
Periodic solutions of arbitrary length in a simple integer iteration |
| title_short |
Periodic solutions of arbitrary length in a simple integer iteration |
| title_full |
Periodic solutions of arbitrary length in a simple integer iteration |
| title_fullStr |
Periodic solutions of arbitrary length in a simple integer iteration |
| title_full_unstemmed |
Periodic solutions of arbitrary length in a simple integer iteration |
| title_sort |
periodic solutions of arbitrary length in a simple integer iteration |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1839 1687-1847 |
| publishDate |
2006-01-01 |
| description |
<p/> <p>We prove that all solutions to the nonlinear second-order difference equation in integers <it>y</it><sub><it>n</it>+1</sub> = ⌈<it>ay</it><sub><it>n</it></sub>⌉-<it>y</it><sub><it>n</it>-1</sub>, {<it>a</it> ∈ ℝ:|<it>a</it>|<2, <it>a</it>≠0,±1}, <it>y</it><sub>0</sub>, <it>y</it><sub>1</sub> ∈ ℤ, are periodic. The first-order system representation of this equation is shown to have self-similar and chaotic solutions in the integer plane.</p> |
| url |
http://www.advancesindifferenceequations.com/content/2006/035847 |
| work_keys_str_mv |
AT clarkdean periodicsolutionsofarbitrarylengthinasimpleintegeriteration |
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1725387212107808768 |