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Normal Forms of Maps: Formal and Algebraic Aspects

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Abstract

We survey and discuss Poincaré–Dulac normal forms of maps near a fixed point. The presentation is accessible with no particular prerequisites. After some introductory material and general results (mostly known facts) we turn to further normalization in the simple resonance case and to formal and analytic infinitesimal symmetries.

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Authors and Affiliations

  1. Dipartimento di Matematica, Universita di Cagliari, via Ospedale 72, 09124, Cagliari, Italy

    Todor Gramchev

  2. Lehrstuhl A für Mathematik, RWTH Aachen, 52056, Aachen, Germany

    Sebastian Walcher

Authors
  1. Todor Gramchev
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  2. Sebastian Walcher
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Correspondence to Todor Gramchev.

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Mathematics Subject Classifications (2000)

37G05, 39A11.

Todor Gramchev: The author is supported by a NATO grant PST.CLG.979347 and GNAMPA–INDAM, Italy.

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Gramchev, T., Walcher, S. Normal Forms of Maps: Formal and Algebraic Aspects. Acta Appl Math 87, 123–146 (2005). https://doi.org/10.1007/s10440-005-1140-2

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  • DOI: https://doi.org/10.1007/s10440-005-1140-2

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