𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Singularity confinement and algebraic entropy: the case of the discrete Painlevé equations

✍ Scribed by Y. Ohta; K.M. Tamizhmani; B. Grammaticos; A. Ramani

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
64 KB
Volume
262
Category
Article
ISSN
0375-9601

No coin nor oath required. For personal study only.

✦ Synopsis

We examine the validity of the results obtained with the singularity confinement integrability criterion in the case of discrete Painleve equations. The method used is based on the requirement of non-exponential growth of the homogeneous degree of the iterate of the mapping. We show that when we start from an integrable autonomous mapping and deautonomise it using singularity confinement the degrees of growth of the nonautonomous mapping and of the autonomous one are identical. Thus this low-growth based approach is compatible with the integrability of the results obtained through singularity confinement. The origin of the singularity confinement property and its necessary character for integrability are also analysed.

📜 SIMILAR VOLUMES

The road to the discrete analogue of the
The road to the discrete analogue of the Painlevé property: Nevanlinna meets singularity confinement
✍ A. Ramani; B. Grammaticos; T. Tamizhmani; K.M. Tamizhmani 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 998 KB

The question of integrability of discrete systems is analysed in the light of the recent findings of Ablowitz et al., who have conjectured that a fast growth of the solutions of a difference equation is an indication of nonintegrability. The study of the behaviour of the solutions of a mapping is ba

On a novel q-discrete analogue of the Pa
On a novel q-discrete analogue of the Painlevé VI equation
✍ B. Grammaticos; A. Ramani 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 61 KB

We present the discrete, q-, form of the Painleve VI equation written as a three-point mapping and analyse the structure óf its singularities. This discrete equation goes over to P at the continuous limit and degenerates towards the discrete q-P VI V through coalescence. It possesses special solutio