Set-oriented numerical computation of rotation sets

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We establish a set-oriented algorithm for the numerical approximation
of the rotation set of homeomorphisms of the two-torus homotopic to
the identity. A theoretical background is given by the concept of ε-rotation
sets. These are obtained by replacing orbits with ε-pseudo-orbits in the definition
of the Misiurewicz-Ziemian rotation set and are shown to converge to the
latter as ε decreases to zero. Based on this result, we prove the convergence
of the numerical approximations as precision and iteration time tend to infinity.
Further, we provide analytic error estimates for the algorithm under an
additional boundedness assumption, which is known to hold in many relevant
cases and in particular for non-empty interior rotation sets.
Original languageEnglish
JournalJournal of Computational Dynamics
Volume4
Issue number1
Pages (from-to)119-141
Number of pages23
ISSN2158-2491
DOIs
Publication statusPublished - 01.11.2017

Bibliographical note

Publisher Copyright:
© American Institute of Mathematical Sciences.

    Research areas

  • Mathematics - Rotation Theory, rotation sets, pseudo-orbits, set-oriented numerics

DOI

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