Distribution of the displacement sequence of an orientation preserving circle homeomorphism - Publikacja - MOST Wiedzy

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Distribution of the displacement sequence of an orientation preserving circle homeomorphism

Abstrakt

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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Wacław Marzantowicz, Justyna Signerska-Rynkowska. (2014). Distribution of the displacement sequence of an orientation preserving circle homeomorphism, 29(2), 153-166. https://doi.org/10.1080/14689367.2013.868867

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Kategoria:
Publikacja w czasopiśmie
Typ:
artykuł w czasopiśmie wyróżnionym w JCR
Opublikowano w:
DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL nr 29, wydanie 2, strony 153 - 166,
ISSN: 1468-9367
Język:
angielski
Rok wydania:
2014
Opis bibliograficzny:
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

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