Abstract
As a conclusion, let us emphasize the underlying arithmetic structure and the interaction between the geometric and symbolic nature of the dynamical systems we have considered throughout this book. We are mainly interested in the two following problems: first, finding geometric interpretations of various symbolic dynamical systems including those generated by substitutions, and secondly, developing multidimensional continued fraction algorithms reflecting the dynamics of the systems.
This chapter has been written by P. Arnoux and V. Berthé
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© 2002 Springer-Verlag Berlin Heidelberg
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(2002). Some open problems. In: Fogg, N.P., Berthé, V., Ferenczi, S., Mauduit, C., Siegel, A. (eds) Substitutions in Dynamics, Arithmetics and Combinatorics. Lecture Notes in Mathematics, vol 1794. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45714-3_12
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DOI: https://doi.org/10.1007/3-540-45714-3_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44141-0
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