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Evgeny Verbitskiy

Mathematical Institute, University of Leiden
PO Box 9512, 2300 RA Leiden, The Netherlands

Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen
PO Box 407, 9700 AK, Groningen, The Netherlands


Schmidt K., Verbitskiy E.
New directions in algebraic dynamical systems
2011, vol. 16, no. 1-2, pp.  79-89
The logarithmic Mahler measure of certain multivariate polynomials occurs frequently as the entropy or the free energy of solvable lattice models (especially dimer models). It is also known that the entropy of an algebraic dynamical system is the logarithmic Mahler measure of the defining polynomial. The connection between the lattice models and the algebraic dynamical systems is still rather mysterious.
Keywords: dimer matchings, domino tilings, Mahler measure, algebraic dynamics, homoclinic points
Citation: Schmidt K., Verbitskiy E.,  New directions in algebraic dynamical systems, Regular and Chaotic Dynamics, 2011, vol. 16, no. 1-2, pp. 79-89
Takens F., Verbitskiy E.
Multifractal Analysis of Dimensions and Entropies
2000, vol. 5, no. 4, pp.  361-382
The theory of dynamical systems has undergone a dramatical revolution in the 20th century. The beauty and power of the theory of dynamical systems is that it links together different areas of mathematics and physics.
In the last 30 years a great deal of attention was dedicated to a statistical description of strange attractors. This led to the development of notions of various dimensions and entropies, which can be associated to the attractor, dynamical system or invariant measure.
In this paper we review these notions and discuss relations between those, among which the most prominent is the so-called multifractal formalism.
Citation: Takens F., Verbitskiy E.,  Multifractal Analysis of Dimensions and Entropies, Regular and Chaotic Dynamics, 2000, vol. 5, no. 4, pp. 361-382

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