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Nonlocal operators are chaotic

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Nonlocal operators are chaotic

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Lizama, C.; Murillo Arcila, M.; Peris Manguillot, A. (2020). Nonlocal operators are chaotic. Chaos An Interdisciplinary Journal of Nonlinear Science. 30(10):1-8. https://doi.org/10.1063/5.0018408

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Título: Nonlocal operators are chaotic
Autor: Lizama, Carlos Murillo Arcila, Marina Peris Manguillot, Alfredo
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
[EN] We characterize for the first time the chaotic behavior of nonlocal operators that come from a broad class of time-stepping schemes of approximation for fractional differential operators. For that purpose, we use ...[+]
Palabras clave: Non-local operators , Chaos , Linear dynamics
Derechos de uso: Reserva de todos los derechos
Fuente:
Chaos An Interdisciplinary Journal of Nonlinear Science. (issn: 1054-1500 )
DOI: 10.1063/5.0018408
Editorial:
American Institute of Physics
Versión del editor: https://doi.org/10.1063/5.0018408
Código del Proyecto:
info:eu-repo/grantAgreement/GVA//GV%2F2018%2F110/
info:eu-repo/grantAgreement/FONDECYT//1180041/
info:eu-repo/grantAgreement/MINECO//MTM2016-75963-P/ES/DINAMICA DE OPERADORES/
info:eu-repo/grantAgreement/GVA//PROMETEO%2F2017%2F102/ES/ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONES/
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-105011GB-I00/ES/DINAMICA DE OPERADORES/
Agradecimientos:
C. Lizama is partially supported by FONDECYT (Grant No. 1180041) and DICYT, Universidad de Santiago de Chile, USACH. M. Murillo-Arcila is supported by MICINN and FEDER, Projects MTM2016-75963-P and PID2019-105011GB-I00, ...[+]
Tipo: Artículo

References

Abadias, L., & Miana, P. J. (2018). Generalized Cesàro operators, fractional finite differences and Gamma functions. Journal of Functional Analysis, 274(5), 1424-1465. doi:10.1016/j.jfa.2017.10.010

Atici, F. M., & Eloe, P. (2009). Discrete fractional calculus with the nabla operator. Electronic Journal of Qualitative Theory of Differential Equations, (3), 1-12. doi:10.14232/ejqtde.2009.4.3

Atıcı, F. M., & Eloe, P. W. (2011). Two-point boundary value problems for finite fractional difference equations. Journal of Difference Equations and Applications, 17(4), 445-456. doi:10.1080/10236190903029241 [+]
Abadias, L., & Miana, P. J. (2018). Generalized Cesàro operators, fractional finite differences and Gamma functions. Journal of Functional Analysis, 274(5), 1424-1465. doi:10.1016/j.jfa.2017.10.010

Atici, F. M., & Eloe, P. (2009). Discrete fractional calculus with the nabla operator. Electronic Journal of Qualitative Theory of Differential Equations, (3), 1-12. doi:10.14232/ejqtde.2009.4.3

Atıcı, F. M., & Eloe, P. W. (2011). Two-point boundary value problems for finite fractional difference equations. Journal of Difference Equations and Applications, 17(4), 445-456. doi:10.1080/10236190903029241

Atici, F. M., & Eloe, P. W. (2008). Initial value problems in discrete fractional calculus. Proceedings of the American Mathematical Society, 137(03), 981-989. doi:10.1090/s0002-9939-08-09626-3

Atıcı, F. M., & Şengül, S. (2010). Modeling with fractional difference equations. Journal of Mathematical Analysis and Applications, 369(1), 1-9. doi:10.1016/j.jmaa.2010.02.009

Banks, J., Brooks, J., Cairns, G., Davis, G., & Stacey, P. (1992). On Devaney’s Definition of Chaos. The American Mathematical Monthly, 99(4), 332-334. doi:10.1080/00029890.1992.11995856

Baranov, A., & Lishanskii, A. (2016). Hypercyclic Toeplitz Operators. Results in Mathematics, 70(3-4), 337-347. doi:10.1007/s00025-016-0527-x

Bayart, F., & Matheron, E. (2009). Dynamics of Linear Operators. doi:10.1017/cbo9780511581113

DELAUBENFELS, R., & EMAMIRAD, H. (2001). Chaos for functions of discrete and continuous weighted shift operators. Ergodic Theory and Dynamical Systems, 21(05). doi:10.1017/s0143385701001675

Edelman, M. (2014). Caputo standard α-family of maps: Fractional difference vs. fractional. Chaos: An Interdisciplinary Journal of Nonlinear Science, 24(2), 023137. doi:10.1063/1.4885536

Edelman, M. (2015). On the fractional Eulerian numbers and equivalence of maps with long term power-law memory (integral Volterra equations of the second kind) to Grünvald-Letnikov fractional difference (differential) equations. Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(7), 073103. doi:10.1063/1.4922834

Edelman, M. (2015). Fractional Maps and Fractional Attractors. Part II: Fractional Difference Caputo α- Families of Maps. The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity, 4(4), 391-402. doi:10.5890/dnc.2015.11.003

Erbe, L., Goodrich, C. S., Jia, B., & Peterson, A. (2016). Survey of the qualitative properties of fractional difference operators: monotonicity, convexity, and asymptotic behavior of solutions. Advances in Difference Equations, 2016(1). doi:10.1186/s13662-016-0760-3

Ferreira, R. A. C. (2012). A discrete fractional Gronwall inequality. Proceedings of the American Mathematical Society, 140(5), 1605-1612. doi:10.1090/s0002-9939-2012-11533-3

Ferreira, R. A. C. (2013). Existence and uniqueness of solution to some discrete fractional boundary value problems of order less than one. Journal of Difference Equations and Applications, 19(5), 712-718. doi:10.1080/10236198.2012.682577

Goodrich, C., & Peterson, A. C. (2015). Discrete Fractional Calculus. doi:10.1007/978-3-319-25562-0

Goodrich, C. S. (2012). On discrete sequential fractional boundary value problems. Journal of Mathematical Analysis and Applications, 385(1), 111-124. doi:10.1016/j.jmaa.2011.06.022

Goodrich, C. S. (2014). A convexity result for fractional differences. Applied Mathematics Letters, 35, 58-62. doi:10.1016/j.aml.2014.04.013

Goodrich, C., & Lizama, C. (2020). A transference principle for nonlocal operators using a convolutional approach: fractional monotonicity and convexity. Israel Journal of Mathematics, 236(2), 533-589. doi:10.1007/s11856-020-1991-2

Gray, H. L., & Zhang, N. F. (1988). On a new definition of the fractional difference. Mathematics of Computation, 50(182), 513-529. doi:10.1090/s0025-5718-1988-0929549-2

Li, K., Peng, J., & Jia, J. (2012). Cauchy problems for fractional differential equations with Riemann–Liouville fractional derivatives. Journal of Functional Analysis, 263(2), 476-510. doi:10.1016/j.jfa.2012.04.011

Lizama, C. (2017). The Poisson distribution, abstract fractional difference equations, and stability. Proceedings of the American Mathematical Society, 145(9), 3809-3827. doi:10.1090/proc/12895

Lizama, C. (2015). lp-maximal regularity for fractional difference equations on UMD spaces. Mathematische Nachrichten, 288(17-18), 2079-2092. doi:10.1002/mana.201400326

Lizama, C., & Murillo-Arcila, M. (2020). Discrete maximal regularity for volterra equations and nonlocal time-stepping schemes. Discrete & Continuous Dynamical Systems - A, 40(1), 509-528. doi:10.3934/dcds.2020020

Martínez-Giménez, F. (2007). Chaos for power series of backward shift operators. Proceedings of the American Mathematical Society, 135(6), 1741-1752. doi:10.1090/s0002-9939-07-08658-3

Radwan, A. G., AbdElHaleem, S. H., & Abd-El-Hafiz, S. K. (2016). Symmetric encryption algorithms using chaotic and non-chaotic generators: A review. Journal of Advanced Research, 7(2), 193-208. doi:10.1016/j.jare.2015.07.002

Radwan, A. G., Moaddy, K., Salama, K. N., Momani, S., & Hashim, I. (2014). Control and switching synchronization of fractional order chaotic systems using active control technique. Journal of Advanced Research, 5(1), 125-132. doi:10.1016/j.jare.2013.01.003

Wu, G.-C., & Baleanu, D. (2013). Discrete fractional logistic map and its chaos. Nonlinear Dynamics, 75(1-2), 283-287. doi:10.1007/s11071-013-1065-7

Wu, G.-C., Baleanu, D., & Zeng, S.-D. (2014). Discrete chaos in fractional sine and standard maps. Physics Letters A, 378(5-6), 484-487. doi:10.1016/j.physleta.2013.12.010

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