P-adic Deterministic and Random Dynamics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2004
|
| Schriftenreihe: | Mathematics and Its Applications
574 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | ?eldK(and,forexample,p-adicsuperspaces). LateronI.V.Volovichproposed the ?rst model ofp-adic string, see Chapter 1. We also remark that the non-Archimedean theory of dynamical systems is a very natural ?eld for applications of non-Archimedean analysis—analysis for mapsf : K? K, see Chapter 1. In 1997, see [101], A. Yu. Khrennikov proposed to applyp-adic dynamical systemsformodelingofcognitiveprocesses. Inapplicationsofp-adicnumbers to cognitive science the crucial role is played not by the algebraic structure of Q , but by its tree-like hierarchical structure. This structure of a p-adic tree p is used for a hierarchical coding of mental information and the parameter p characterizesthecodingsystemofacognitivesystem. Therefore,insuchp-adic cognitive models the assumption thatp is a prime number is not so natural. We can apply dynamical systems in rings ofp-adic numbersQ , wherep> 1 is an p arbitrarynaturalnumber. Foundationsofp-adiccognitivemodelsarepresented in detail in the book [111], see also Chapter 8, Chapter 11, and Chapter 12 for new developments of this theory. ThisbookismainlybasedontheresultsofinvestigationsoftheVaxj ¨ og ¨ roupin p-adic dynamical systems: Professor Andrei Yu. Khrennikov and the graduate students Karl-Olof Lindahl, Marcus Nilsson, Robert Nyqvist, and Per-Anders Svensson. One of the main streams in the research of the V¨ axj¨ o group was induced by an observation, see [101], that in the theory ofp-adic dynamical systems there appearsa new important parameter - the prime numberp giving the basis of the corresponding number ?eld Q . Therefore it may be interesting to investigate p dependence of some characteristics of a dynamical system on p, especially whenp?? |
| Beschreibung: | 1 Online-Ressource (XVIII, 270 p) |
| ISBN: | 9781402026607 9789048166985 |
| DOI: | 10.1007/978-1-4020-2660-7 |
Internformat
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Datensatz im Suchindex
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| author | Khrennikov, Andrei Yu |
| author_facet | Khrennikov, Andrei Yu |
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| author_sort | Khrennikov, Andrei Yu |
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| dewey-ones | 512 - Algebra |
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| dewey-sort | 3512.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4020-2660-7 |
| format | Electronic eBook |
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| isbn | 9781402026607 9789048166985 |
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| spelling | Khrennikov, Andrei Yu Verfasser aut P-adic Deterministic and Random Dynamics by Andrei Yu. Khrennikov, Marcus Nilson Dordrecht Springer Netherlands 2004 1 Online-Ressource (XVIII, 270 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 574 ?eldK(and,forexample,p-adicsuperspaces). LateronI.V.Volovichproposed the ?rst model ofp-adic string, see Chapter 1. We also remark that the non-Archimedean theory of dynamical systems is a very natural ?eld for applications of non-Archimedean analysis—analysis for mapsf : K? K, see Chapter 1. In 1997, see [101], A. Yu. Khrennikov proposed to applyp-adic dynamical systemsformodelingofcognitiveprocesses. Inapplicationsofp-adicnumbers to cognitive science the crucial role is played not by the algebraic structure of Q , but by its tree-like hierarchical structure. This structure of a p-adic tree p is used for a hierarchical coding of mental information and the parameter p characterizesthecodingsystemofacognitivesystem. Therefore,insuchp-adic cognitive models the assumption thatp is a prime number is not so natural. We can apply dynamical systems in rings ofp-adic numbersQ , wherep> 1 is an p arbitrarynaturalnumber. Foundationsofp-adiccognitivemodelsarepresented in detail in the book [111], see also Chapter 8, Chapter 11, and Chapter 12 for new developments of this theory. ThisbookismainlybasedontheresultsofinvestigationsoftheVaxj ¨ og ¨ roupin p-adic dynamical systems: Professor Andrei Yu. Khrennikov and the graduate students Karl-Olof Lindahl, Marcus Nilsson, Robert Nyqvist, and Per-Anders Svensson. One of the main streams in the research of the V¨ axj¨ o group was induced by an observation, see [101], that in the theory ofp-adic dynamical systems there appearsa new important parameter - the prime numberp giving the basis of the corresponding number ?eld Q . Therefore it may be interesting to investigate p dependence of some characteristics of a dynamical system on p, especially whenp?? Mathematics Geometry, algebraic Field theory (Physics) Functional analysis Mathematical physics Consciousness Field Theory and Polynomials Mathematical Methods in Physics Cognitive Psychology Functional Analysis Algebraic Geometry Mathematik Mathematische Physik Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf p-adische Analysis (DE-588)4252360-6 gnd rswk-swf p-adische Analysis (DE-588)4252360-6 s Differenzierbares dynamisches System (DE-588)4137931-7 s 1\p DE-604 Nilson, Marcus Sonstige oth https://doi.org/10.1007/978-1-4020-2660-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Khrennikov, Andrei Yu P-adic Deterministic and Random Dynamics Mathematics Geometry, algebraic Field theory (Physics) Functional analysis Mathematical physics Consciousness Field Theory and Polynomials Mathematical Methods in Physics Cognitive Psychology Functional Analysis Algebraic Geometry Mathematik Mathematische Physik Differenzierbares dynamisches System (DE-588)4137931-7 gnd p-adische Analysis (DE-588)4252360-6 gnd |
| subject_GND | (DE-588)4137931-7 (DE-588)4252360-6 |
| title | P-adic Deterministic and Random Dynamics |
| title_auth | P-adic Deterministic and Random Dynamics |
| title_exact_search | P-adic Deterministic and Random Dynamics |
| title_full | P-adic Deterministic and Random Dynamics by Andrei Yu. Khrennikov, Marcus Nilson |
| title_fullStr | P-adic Deterministic and Random Dynamics by Andrei Yu. Khrennikov, Marcus Nilson |
| title_full_unstemmed | P-adic Deterministic and Random Dynamics by Andrei Yu. Khrennikov, Marcus Nilson |
| title_short | P-adic Deterministic and Random Dynamics |
| title_sort | p adic deterministic and random dynamics |
| topic | Mathematics Geometry, algebraic Field theory (Physics) Functional analysis Mathematical physics Consciousness Field Theory and Polynomials Mathematical Methods in Physics Cognitive Psychology Functional Analysis Algebraic Geometry Mathematik Mathematische Physik Differenzierbares dynamisches System (DE-588)4137931-7 gnd p-adische Analysis (DE-588)4252360-6 gnd |
| topic_facet | Mathematics Geometry, algebraic Field theory (Physics) Functional analysis Mathematical physics Consciousness Field Theory and Polynomials Mathematical Methods in Physics Cognitive Psychology Functional Analysis Algebraic Geometry Mathematik Mathematische Physik Differenzierbares dynamisches System p-adische Analysis |
| url | https://doi.org/10.1007/978-1-4020-2660-7 |
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