On 2- and 3-periodic Lyness difference equations
We describe the sequences {xn}n given by the non-autonomous second order Lyness difference equations xn+2 = (an + xn+1)/xn, where {an}n is either a 2-periodic or a 3-periodic sequence of positive values and the initial conditions x1, x2 are as well positive. We also show an interesting phenomenon of...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2012 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:150564 |
| Online Access: | https://ddd.uab.cat/record/150564 https://dx.doi.org/urn:doi:10.1080/10236198.2010.524212 |
| Access Level: | Open access |
| Keyword: | Difference equations with periodic coefficients Circle maps Rotation number |
| Summary: | We describe the sequences {xn}n given by the non-autonomous second order Lyness difference equations xn+2 = (an + xn+1)/xn, where {an}n is either a 2-periodic or a 3-periodic sequence of positive values and the initial conditions x1, x2 are as well positive. We also show an interesting phenomenon of the discrete dynamical systems associated to some of these difference equations: the existence of one oscillation of their associated rotation number functions. This behavior does not appear for the autonomous Lyness difference equations. |
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