Logistic Map Potentials

We develop and illustrate methods to compute all single particle potentials that underlie the logistic map, x --> sx(1-x) for 0<s<=4. We show that the switchback potentials can be obtained from the primary potential through functional transformations. We are thereby able to produce the vari...

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Detalles Bibliográficos
Autores principales: Curtright, Thomas, Veitia, Andrzej
Lenguaje:eng
Publicado: 2010
Materias:
Mathematical Physics and Mathematics
Acceso en línea:https://dx.doi.org/10.1016/j.physleta.2010.11.019
http://cds.cern.ch/record/1268288
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author Curtright, Thomas
Veitia, Andrzej
author_facet Curtright, Thomas
Veitia, Andrzej
author_sort Curtright, Thomas
collection CERN
description We develop and illustrate methods to compute all single particle potentials that underlie the logistic map, x --> sx(1-x) for 0<s<=4. We show that the switchback potentials can be obtained from the primary potential through functional transformations. We are thereby able to produce the various branches of the corresponding analytic potential functions, which have an infinite number of branch points for generic s>2. We illustrate the methods numerically for the cases s=5/2 and s=10/3.
id cern-1268288
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2010
record_format invenio
spelling cern-12682882023-03-12T20:50:09Zdoi:10.1016/j.physleta.2010.11.019http://cds.cern.ch/record/1268288engCurtright, ThomasVeitia, AndrzejLogistic Map PotentialsMathematical Physics and MathematicsWe develop and illustrate methods to compute all single particle potentials that underlie the logistic map, x --> sx(1-x) for 0<s<=4. We show that the switchback potentials can be obtained from the primary potential through functional transformations. We are thereby able to produce the various branches of the corresponding analytic potential functions, which have an infinite number of branch points for generic s>2. We illustrate the methods numerically for the cases s=5/2 and s=10/3.We develop and illustrate methods to compute all single particle potentials that underlie the logistic map, x --> sx(1-x) for 0<s<=4. We show that the switchback potentials can be obtained from the primary potential through functional transformations. We are thereby able to produce the various branches of the corresponding analytic potential functions, which have an infinite number of branch points for generic s>2. We illustrate the methods numerically for the cases s=5/2 and s=10/3.arXiv:1005.5030CERN-PH-TH-2010-123UMTG-15CERN-PH-TH-2010-123UMTH-15oai:cds.cern.ch:12682882010-05-28
spellingShingle Mathematical Physics and Mathematics
Curtright, Thomas
Veitia, Andrzej
Logistic Map Potentials
title Logistic Map Potentials
title_full Logistic Map Potentials
title_fullStr Logistic Map Potentials
title_full_unstemmed Logistic Map Potentials
title_short Logistic Map Potentials
title_sort logistic map potentials
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1016/j.physleta.2010.11.019
http://cds.cern.ch/record/1268288
work_keys_str_mv AT curtrightthomas logisticmappotentials
AT veitiaandrzej logisticmappotentials

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