Pointwise periodic maps with quantized first integrals

Anna Cimà; Armengol Gasull; Víctor Mañosa Fernández

doi:10.1016/j.cnsns.2021.106150

Pointwise periodic maps with quantized first integrals

Anna Cimà, Armengol Gasull, Víctor Mañosa Fernández

Research output: Contribution to journal › Article › Research › peer-review

1 Citation (Scopus)

Abstract

We describe the global dynamics of some pointwise periodic piecewise linear maps in the plane that exhibit interesting dynamic features. For each of these maps we find a first integral. For these integrals the set of values are discrete, thus quantized. Furthermore, the level sets are bounded sets whose interior is formed by a finite number of open tiles of certain regular or uniform tessellations. The action of the maps on each invariant set of tiles is described geometrically.

Original language	English
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	108
DOIs	https://doi.org/10.1016/j.cnsns.2021.106150
Publication status	Published - 2022

Keywords

Periodic points
Pointwise periodic maps
Piecewise linear maps
Quantized first integrals
Regular and uniform tessellations

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10.1016/j.cnsns.2021.106150

https://ddd.uab.cat/record/257129

STUDY OF CONTINUOUS AND DISCRETE DYNAMIC SYSTEMS WITH EMPHASIS ON THEIR BIFURCATIONS, PERIODIC ORBITS AND INTEGRABILITY
Llibre Salo, J. (Principal Investigator), Torregrosa i Arús, J. (Co-Investigador/a Principal), Cufi Cabre, C. (Collaborator), Carvalho, Y. R. (Collaborator), Cousillas, G. (Collaborator), Diz Pita, É. (Collaborator), Ferragut Amengual, A. M. (Collaborator), GOUVEIA, L. F. D. S. (Collaborator), Iván Sánchez Sánchez (Collaborator), Jiménez Ruíz, J. J. (Collaborator), RODERO, A. L. (Collaborator), Ramírez, V. (Collaborator), Artes Ferragud, J. C. (Investigator), Caubergh , M. M. (Investigator), Cima Mollet, A. M. (Investigator), Corbera Subirana, M. (Investigator), Cors Iglesias, J. M. (Investigator), Gasull Embid, A. (Investigator), Pantazi ., C. (Investigator), Soler Villanueva, J. (Investigator), Garrido Pelaez, J. M. (Collaborator) & Valls Anglés, C. (Collaborator)
1/06/20 → 29/02/24
Project: Research Projects and Other Grants
Sistemas dinámicos en baja dimensión y aplicaciones
Alseda Soler, L. (Principal Investigator), Rojas Perez, D. (Collaborator), Romero Sánchez, D. (Collaborator), Juher Barrot, D. (Investigator), Mañosas Capellades, F. (Investigator), Mondelo Gonzalez, J. M. (Investigator) & Borros Cullell, S. (Collaborator)
Spanish Ministry of Economy and Competitiveness (MINECO), Ministerio de Ciencia e Innovación (MICINN)
1/01/18 → 30/09/21
Project: Research Projects and Other Grants

Cite this

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title = "Pointwise periodic maps with quantized first integrals",

abstract = "We describe the global dynamics of some pointwise periodic piecewise linear maps in the plane that exhibit interesting dynamic features. For each of these maps we find a first integral. For these integrals the set of values are discrete, thus quantized. Furthermore, the level sets are bounded sets whose interior is formed by a finite number of open tiles of certain regular or uniform tessellations. The action of the maps on each invariant set of tiles is described geometrically.",

keywords = "Periodic points, Pointwise periodic maps, Piecewise linear maps, Quantized first integrals, Regular and uniform tessellations",

author = "Anna Cim{\`a} and Armengol Gasull and {Ma{\~n}osa Fern{\'a}ndez}, V{\'i}ctor",

year = "2022",

doi = "10.1016/j.cnsns.2021.106150",

language = "English",

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T1 - Pointwise periodic maps with quantized first integrals

AU - Cimà, Anna

AU - Gasull, Armengol

AU - Mañosa Fernández, Víctor

PY - 2022

Y1 - 2022

N2 - We describe the global dynamics of some pointwise periodic piecewise linear maps in the plane that exhibit interesting dynamic features. For each of these maps we find a first integral. For these integrals the set of values are discrete, thus quantized. Furthermore, the level sets are bounded sets whose interior is formed by a finite number of open tiles of certain regular or uniform tessellations. The action of the maps on each invariant set of tiles is described geometrically.

AB - We describe the global dynamics of some pointwise periodic piecewise linear maps in the plane that exhibit interesting dynamic features. For each of these maps we find a first integral. For these integrals the set of values are discrete, thus quantized. Furthermore, the level sets are bounded sets whose interior is formed by a finite number of open tiles of certain regular or uniform tessellations. The action of the maps on each invariant set of tiles is described geometrically.

KW - Periodic points

KW - Pointwise periodic maps

KW - Piecewise linear maps

KW - Quantized first integrals

KW - Regular and uniform tessellations

U2 - 10.1016/j.cnsns.2021.106150

DO - 10.1016/j.cnsns.2021.106150

M3 - Article

SN - 1007-5704

VL - 108

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

ER -

Pointwise periodic maps with quantized first integrals

Abstract

Keywords

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Projects

STUDY OF CONTINUOUS AND DISCRETE DYNAMIC SYSTEMS WITH EMPHASIS ON THEIR BIFURCATIONS, PERIODIC ORBITS AND INTEGRABILITY

Sistemas dinámicos en baja dimensión y aplicaciones

Cite this