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Growth and integrability in the dynamics of mappings

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Abstract

The growth of some numerical characteristics of the mappings under their iterations in the context of the general problem of integrability is discussed. In the general case such characteristics as complexity by Arnold or the number of the different images for the multiple-valued mappings are growing exponentially. It is shown that the integrability is closely related with thepolynomial growth. The analogies with quantum integrable systems are discussed.

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Authors and Affiliations

  1. Department of Mathematics and Mechanics, Moscow State University, SU-119899, Moscow, USSR

    Alexander P. Veselov

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  1. Alexander P. Veselov
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Communicated by N. Yu. Reshetikhin

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Veselov, A.P. Growth and integrability in the dynamics of mappings. Commun.Math. Phys. 145, 181–193 (1992). https://doi.org/10.1007/BF02099285

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  • DOI: https://doi.org/10.1007/BF02099285

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