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Differential Equations, Chaos and Variational Problems pp 317–344Cite as

Some New Concepts of Dimension

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Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 75))

Abstract

This paper contains a review of recent results concerning some new concepts of analytical dimensions of sets and measures. We make in evidence the relationship between these new concepts and the classical once. In particular we give some results concerning estimates, variational principles and generic properties. Finally, we give some applications in the theory of iterated function systems and the theory of differential equations.

To Arrigo Cellina and James Yorke

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Author information

Authors and Affiliations

  1. WMS AGH, Al. Mickiewicza 30, PL-30059, Kraków, Poland

    Józef Myjak

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  1. Józef Myjak
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal

    Vasile Staicu

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Myjak, J. (2007). Some New Concepts of Dimension. In: Staicu, V. (eds) Differential Equations, Chaos and Variational Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 75. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8482-1_25

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