Cantor staircases in physics and diophantine approximations

For a wide class of dynamical systems the variables involved relate to one another through a Cantor staircase function. When they are time variables, the staircases have well-known universal properties that suggest a connection with certain classical problems in Number Theory. In this paper we exten...

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Autor principal: Grynberg, Sebastian Pablo
Publicado: 1998
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02181274_v8_n6_p1095_PiacquadioLosada
http://hdl.handle.net/20.500.12110/paper_02181274_v8_n6_p1095_PiacquadioLosada
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_02181274_v8_n6_p1095_PiacquadioLosada
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spelling paper:paper_02181274_v8_n6_p1095_PiacquadioLosada2023-06-08T15:21:20Z Cantor staircases in physics and diophantine approximations Grynberg, Sebastian Pablo For a wide class of dynamical systems the variables involved relate to one another through a Cantor staircase function. When they are time variables, the staircases have well-known universal properties that suggest a connection with certain classical problems in Number Theory. In this paper we extend some of those universal properties to certain Cantor staircases that appear in Quantum Mechanics, where the variables involved are not time variables. We also develop some connections between the geometry of these Cantor staircases and the problem of approximating irrational numbers by rational ones, classical in Number Theory. Fil:Grynberg, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1998 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02181274_v8_n6_p1095_PiacquadioLosada http://hdl.handle.net/20.500.12110/paper_02181274_v8_n6_p1095_PiacquadioLosada
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description For a wide class of dynamical systems the variables involved relate to one another through a Cantor staircase function. When they are time variables, the staircases have well-known universal properties that suggest a connection with certain classical problems in Number Theory. In this paper we extend some of those universal properties to certain Cantor staircases that appear in Quantum Mechanics, where the variables involved are not time variables. We also develop some connections between the geometry of these Cantor staircases and the problem of approximating irrational numbers by rational ones, classical in Number Theory.
author Grynberg, Sebastian Pablo
spellingShingle Grynberg, Sebastian Pablo
Cantor staircases in physics and diophantine approximations
author_facet Grynberg, Sebastian Pablo
author_sort Grynberg, Sebastian Pablo
title Cantor staircases in physics and diophantine approximations
title_short Cantor staircases in physics and diophantine approximations
title_full Cantor staircases in physics and diophantine approximations
title_fullStr Cantor staircases in physics and diophantine approximations
title_full_unstemmed Cantor staircases in physics and diophantine approximations
title_sort cantor staircases in physics and diophantine approximations
publishDate 1998
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02181274_v8_n6_p1095_PiacquadioLosada
http://hdl.handle.net/20.500.12110/paper_02181274_v8_n6_p1095_PiacquadioLosada
work_keys_str_mv AT grynbergsebastianpablo cantorstaircasesinphysicsanddiophantineapproximations
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