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Abstract: We consider some two-dimensional birational transformations. One of them is abirational deformation of the H\-enon map. For some of these birationalmappings, the post critical set i.e. the iterates of the critical set isinfinite and we show that this gives straightforwardly the algebraic covariantcurves of the transformation when they exist. These covariant curves are usedto build the preserved meromorphic two-form. One may have also an infinite postcritical set yielding a covariant curve which is not algebraic transcendent.For two of the birational mappings considered, the post critical set is notinfinite and we claim that there is no algebraic covariant curve and nopreserved meromorphic two-form. For these two mappings with non infinite postcritical sets, attracting sets occur and we show that they pass the usual testsLyapunov exponents and the fractal dimension for being strange attractors.The strange attractor of one of these two mappings is unbounded.



Author: M. Bouamra, S. Hassani, J.-M. Maillard

Source: https://arxiv.org/



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