Asymptotically periodic and bifurcation points in fractional difference maps
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913664991232000 |
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| author | Edelman, Mark |
| author_facet | Edelman, Mark |
| contents | The first step in investigating fractional difference maps, which do not have periodic points except fixed points, is to find asymptotically periodic points and bifurcation points and draw asymptotic bifurcation diagrams. Recently derived equations that allow calculations of asymptotically periodic and bifurcation points contain coefficients defined as slowly converging infinite sums. In this paper we derive analytic expressions for coefficients of the equations that allow calculations of asymptotically periodic and bifurcation points in fractional difference maps. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_20877 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotically periodic and bifurcation points in fractional difference maps Edelman, Mark Dynamical Systems Mathematical Physics Chaotic Dynamics 26A33, 47H99, 34A99, 37G15, 70K50, 39A70 The first step in investigating fractional difference maps, which do not have periodic points except fixed points, is to find asymptotically periodic points and bifurcation points and draw asymptotic bifurcation diagrams. Recently derived equations that allow calculations of asymptotically periodic and bifurcation points contain coefficients defined as slowly converging infinite sums. In this paper we derive analytic expressions for coefficients of the equations that allow calculations of asymptotically periodic and bifurcation points in fractional difference maps. |
| title | Asymptotically periodic and bifurcation points in fractional difference maps |
| topic | Dynamical Systems Mathematical Physics Chaotic Dynamics 26A33, 47H99, 34A99, 37G15, 70K50, 39A70 |
| url | https://arxiv.org/abs/2412.20877 |