The space of initial conditions for linearizable mappings

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Published 13 January 2003 • Published under licence by IOP Publishing Ltd
, , Citation T Takenawa et al 2003 Nonlinearity 16 457 DOI 10.1088/0951-7715/16/2/306

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Author affiliations

1 Graduate School of Mathematical Sciences, University of Tokyo, Komaba 3-8-1, Meguro-ku, Tokyo 153-8914, Japan

2 GMPIB, Université Paris VII, Tour 24-14, 5e étage, case 7021, 75251 Paris, France

3 Department of Applied Mathematics, Faculty of Engineering, Hiroshima University, Kagamiyama 1-4-1, Higashi-Hiroshima, 739-8527, Japan

4 CPT, Ecole Polytechnique, CNRS, UMR 7644, 91128 Palaiseau, France

Dates

  1. Received 5 April 2002
  2. Published

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0951-7715/16/2/457

Abstract

We apply the algebraic–geometric techniques developed for the study of mappings which have the singularity confinement property to mappings which are integrable through linearization. The main difference with respect to the previous studies is that the linearizable mappings have generically unconfined singularities. Despite this fact we are able to provide a complete description of the dynamics of these mappings and derive rigorously their growth properties.

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10.1088/0951-7715/16/2/306