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Abstract
In some applications not only the knowledge of the behaviour of trajectories of a map is important, but also their displacements. We describe in detail the distribution of elements of the displacement sequence along a trajectory of an orientation preserving circle homeomorphism ϕ with irrational rotation number ϱ(ϕ). The values of displacement are dense in a set which depends on the map γ (semi-)conjugating ϕ with the rotation by ϱ(ϕ) and which is the support of the displacement distribution. We provide an effective formula for the density of this distribution if γ is a C1-diffeomorphism. Moreover, we show approximation of the displacement distribution by sample displacements measured for any other circle homeomorphism sufficiently close to the initial homeomorphism ϕ, which constitutes a rigorous proof of numerical results seen in certain integrate-and-fire models.
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Authors (2)
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Wacław Marzantowicz
- adam Mickiewicz University of Poznań .
-
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- Category:
- Articles
- Type:
- artykuł w czasopiśmie wyróżnionym w JCR
- Published in:
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DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL
no. 29,
edition 2,
pages 153 - 166,
ISSN: 1468-9367 - Language:
- English
- Publication year:
- 2014
- Bibliographic description:
- Marzantowicz W., Signerska-Rynkowska J.: Distribution of the displacement sequence of an orientation preserving circle homeomorphism// DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL. -Vol. 29, iss. 2 (2014), s.153-166
- DOI:
- Digital Object Identifier (open in new tab) 10.1080/14689367.2013.868867
- Verified by:
- Gdańsk University of Technology
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