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A Class of Integrable and Nonintegrable Mappings and their Dynamics |
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| Authors: | Teruhisa Tsuda Basil Grammaticos Alfred Ramani Tomoyuki Takenawa |
| Affiliation: | (1) Faculty of Mathematics, Kyushu University, Hakozaki, Fukuoka 812-8581, Japan;(2) IMNC, Université Paris VII & XI, CNRS, UMR 8165, Bat. 104, 91406 Orsay, France;(3) CPT, Ecole Polytechnique, CNRS, UMR 7644, 91128 Palaiseau, France;(4) Faculty of Marine Technology, Tokyo University of Marine Science and Technology, Etchu-jima, Tokyo 135-8533, Japan |
| Abstract: | We analyse a class of mappings which by construction do not belong to the QRT family. We show that some of the members of this class have invariants of high degree. A new linearisable mapping is also identified. A mapping which possesses confined singularities while having nonzero algebraic entropy is presented. Its dynamics are studied in detail and shown to be related intimately to the Fibonacci recurrence. |
| Keywords: | integrability singularity linearisability fibonacci number discrete dynamical system |
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