One-parameter Darboux-deformed Fibonacci numbers

Haret C Rosu; S. C. Mancas; Stefani Mancas

doi:10.1142/S0217732323500220

One-parameter Darboux-deformed Fibonacci numbers

Haret C Rosu, S. C. Mancas, Stefani Mancas

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

Abstract

One-parameter Darboux deformations are effected for the simple ODE satisfied by the continuous generalizations of the Fibonacci sequence recently discussed by Faraoni and Atieh [Symmetry 13, 200 (2021)], who promoted a formal analogy with the Friedmann equation in the FLRW homogeneous cosmology. The method allows the introduction of deformations of the continuous Fibonacci sequences, hence of Darboux-deformed Fibonacci (non integer) numbers. Considering the same ODE as a parametric oscillator equation, the Ermakov-Lewis invariants for these sequences are also discussed.

Original language	American English
Journal	Modern Physics Letters A
Volume	38
DOIs	https://doi.org/10.1142/S0217732323500220
State	Published - Feb 10 2023

Keywords

Darboux deformations
Friedmann equation

Disciplines

Physical Sciences and Mathematics
Applied Mathematics

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10.1142/S0217732323500220License: Unspecified

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N2 - One-parameter Darboux deformations are effected for the simple ODE satisfied by the continuous generalizations of the Fibonacci sequence recently discussed by Faraoni and Atieh [Symmetry 13, 200 (2021)], who promoted a formal analogy with the Friedmann equation in the FLRW homogeneous cosmology. The method allows the introduction of deformations of the continuous Fibonacci sequences, hence of Darboux-deformed Fibonacci (non integer) numbers. Considering the same ODE as a parametric oscillator equation, the Ermakov-Lewis invariants for these sequences are also discussed.

AB - One-parameter Darboux deformations are effected for the simple ODE satisfied by the continuous generalizations of the Fibonacci sequence recently discussed by Faraoni and Atieh [Symmetry 13, 200 (2021)], who promoted a formal analogy with the Friedmann equation in the FLRW homogeneous cosmology. The method allows the introduction of deformations of the continuous Fibonacci sequences, hence of Darboux-deformed Fibonacci (non integer) numbers. Considering the same ODE as a parametric oscillator equation, the Ermakov-Lewis invariants for these sequences are also discussed.

KW - Darboux deformations

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SN - 1793-6632

VL - 38

JO - Modern Physics Letters A

JF - Modern Physics Letters A

ER -

One-parameter Darboux-deformed Fibonacci numbers

Abstract

Keywords

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