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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| Format: | Article |
| Language: | English |
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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 |
| Summary: | <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> |
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| ISSN: | 1687-1839 1687-1847 |