From Pikovsky-Rabinovich Dynamical System to Lagrange-Hamilton Geometrical Objects

Mircea Neagu; Elena Ovsiyuk

doi:10.2478/awutm-2024-0009

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From Pikovsky-Rabinovich Dynamical System to Lagrange-Hamilton Geometrical Objects

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 60 (2024): Issue 1 (January 2024)

By: Mircea Neagu and Elena Ovsiyuk

Open Access

|Nov 2024

Abstract

The aim of this paper is to develop, via the least squares variational method, the Lagrange-Hamilton geometries (in the sense of nonlinear connections, d-torsions and Lagrangian Yang-Mills electromagnetic-like energy) produced by Pikovsky-Rabinovich dynamical system from cryptography. From a geometrical point of view, the Jacobi stability of the Pikovsky-Rabinovich system is discussed.

References

V. Balan, M. Neagu, Jet Single-Time Lagrange Geometry and Its Applications, John Wiley & Sons, Inc., Hoboken, New Jersey, 2011.
Search in Google Scholar Back to article
C. G. Böhmer, T. Harko, S. V. Sabău, Jacobi stability analysis of dynamical systems - applications in gravitation and cosmology, Adv. Theor. Math. Phys. 16 (2012), 1145–1196.
Search in Google Scholar Back to article
I. Bucătaru, R. Miron, Finsler-Lagrange Geometry. Applications to Dynamical Systems, Romanian Academy Eds, Bucharest, 2007.
Search in Google Scholar Back to article
O. Chiş, M. Puta, The dynamics of Rabinovich system, Differential Geometry - Dynamical Systems 10 (2008), 91–98.
Search in Google Scholar Back to article
R. Miron, M. Anastasiei, The Geometry of Lagrange Spaces: Theory and Applications, Kluwer Academic Publishers, Dordrecht, 1994.
Search in Google Scholar Back to article
R. Miron, D. Hrimiuc, H. Shimada, S. V. Sabău, The Geometry of Hamilton and Lagrange Spaces, Kluwer Academic Publishers, Dordrecht, 2001.
Search in Google Scholar Back to article
M. Neagu, A. Oană, Dual Jet Geometrization for Time-Dependent Hamiltonians and Applications, Synthesis Lectures on Mathematics & Statistics, Springer, Cham, Switzerland, 2022.
Search in Google Scholar Back to article
M. Neagu, E. Ovsiyuk, A note on the Jacobi stability of dynamical systems via Lagrange geometry and KCC theory, Proc. of the XVI-th Internat. Virtual Res.-to-Pract. Conf. Innov. Techn. for Teach. Phys., Math. and Vocat. Discipl. (2024), Mozyr State Pedagogical University named after I.P. Shamyakin, Mozyr, Belarus, pp. 229–231.
Search in Google Scholar Back to article
M. Neagu, C. Udrişte, From PDE systems and metrics to multi-time field theories and geometric dynamics, Seminarul de Mecanică 79 (2001), 1–33.
Search in Google Scholar Back to article
A. S. Pikovsky, M. I. Rabinovich, Stochastic oscillations in dissipative systems, Math. Phys. Rev. 2 (1981), 8–24.
Search in Google Scholar Back to article
X. Tong, Y. Liu, M. Zhang, H. Xu, Z. Wang, An image encryption scheme based on hyperchaotic Rabinovich and exponential chaos maps, Entropy 17 (2015), 181–196.
Search in Google Scholar Back to article
C. Udrişte, Geometric Dynamics, Kluwer Academic Publishers, Dordrecht, 2000.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/awutm-2024-0009 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293

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Language: English

Page range: 123 - 129

Submitted on: Sep 1, 2024

Accepted on: Nov 11, 2024

Published on: Nov 21, 2024

Published by: West University of Timisoara

In partnership with: Paradigm Publishing Services

Publication frequency: Volume open

Keywords:

Pikovsky-Rabinovich system,

(co)tangent bundles,

least squares Lagrangian and Hamiltonian,

Lagrange-Hamilton geometries

Related subjects:

Mathematics,

General mathematics

© 2024 Mircea Neagu, Elena Ovsiyuk, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 60 (2024): Issue 1 (January 2024)