Generalized Fibonacci Numbers, Cosmological Analogies, and an Invariant

Faraoni, Valerio; Atieh, Farah

doi:10.3390/sym13020200

Cited by 4 publications

(1 citation statement)

References 13 publications

(20 reference statements)

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“…Extending this theory to the gravitational field on a time scale, we could calculate the interaction field Lagrangians for the electromagnetic and gravitational interactions [26]. Next, we can look for analogies between the Fibonacci sequence and certain spatially homogeneous and isotropic universes in Friedmann-Lemaitre-Robertson-Walker cosmology on time scales [27].…”

Section: Discussionmentioning

confidence: 99%

Symmetries for Nonconservative Field Theories on Time Scale

Postavaru

Toma

2021

Symmetry

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Symmetries and their associated conserved quantities are of great importance in the study of dynamic systems. In this paper, we describe nonconservative field theories on time scales—a model that brings together, in a single theory, discrete and continuous cases. After defining Hamilton’s principle for nonconservative field theories on time scales, we obtain the associated Lagrange equations. Next, based on the Hamilton’s action invariance for nonconservative field theories on time scales under the action of some infinitesimal transformations, we establish symmetric and quasi-symmetric Noether transformations, as well as generalized quasi-symmetric Noether transformations. Once the Noether symmetry selection criteria are defined, the conserved quantities for the nonconservative field theories on time scales are identified. We conclude with two examples to illustrate the applicability of the theory.

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Section: Discussionmentioning

confidence: 99%

Symmetries for Nonconservative Field Theories on Time Scale

Postavaru

Toma

2021

Symmetry

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A Fibonacci-like universe expansion on time-scale

Postavaru

Toma

2022

Chaos, Solitons & Fractals

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One-parameter Darboux-deformed Fibonacci numbers

Rosu

Mancas

2023

Mod. Phys. Lett. A

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One-parameter Darboux deformations are established for the simple ordinary differential equation (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 (noninteger) numbers. Considering the same ODE as a parametric oscillator equation, the Ermakov–Lewis invariants for these sequences are also discussed.

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Generalized Fibonacci Numbers, Cosmological Analogies, and an Invariant

Cited by 4 publications

References 13 publications

Symmetries for Nonconservative Field Theories on Time Scale

Symmetries for Nonconservative Field Theories on Time Scale

A Fibonacci-like universe expansion on time-scale

One-parameter Darboux-deformed Fibonacci numbers

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