Maximally chaotic dynamical systems

Savvidy, George

doi:10.1016/j.aop.2020.168274

Cited by 16 publications

(9 citation statements)

References 83 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…4 Examples of MCDS were discovered and discussed in the earlier investigations by Lobachevsky, Artin, Hadamard, Hedlund, Hopf, Birkhoff and others, [7][8][9][10][11][12][13][14][15][16][17][18][19][21][22][23] as well as in more recent investigations. [24][25][26][27][28][29][30][31][32][33][34][35][36]40 Here we shall introduce and discuss the classical-and quantum-mechanical properties of MCDS, the application of the ergodic theory to the investigation of non-Abelian gauge fields [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58]…”

Section: Introductionmentioning

confidence: 99%

“…This result provides a powerful tool for the investigation of the Hamiltonian systems. 40 If the time evolution of a classical Hamiltonian system under investigation can be reformulated as a geodesic flow on a Riemannian manifold and if all its sectional curvatures are negative, then it represents a MCDS system. The MCDS approach the equilibrium state with exponential rate that depends on the Kolmogorov-Sinai entropy.…”

Section: Introductionmentioning

confidence: 99%

“…41-47, 47, 53, 55-62, 120, 121, 123-126 In the case of space homogeneous gauge fields the Yang-Mills equations reduce to a classical mechanical system, so called Yang-Mills classical mechanics (YMCM), and represent the bosonic part of the matrix models. 47,[56][57][58][59][60][61][62] It has finite degrees of freedom, [41][42][43][44] isotropic and homogeneous energy momentum tensor (40) and relativistic equation of state (41) 3 . 65 By using the energy and momentum conservation integrals the system can be reduced to a system of a lower dimension, and the fundamental question is if the residual system is integrable and has additional hidden conserved integrals 3 or is non-integrable and chaotic.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Maximally Chaotic Dynamical Systems and Fundamental Interactions

Savvidy

2022

Preprint

Self Cite

View full text Add to dashboard Cite

We give a general review on the application of Ergodic theory to the investigation of dynamics of the Yang-Mills gauge fields and of the gravitational systems, as well as its application in the Monte Carlo method and fluid dynamics. In ergodic theory the maximally chaotic dynamical systems (MCDS) can be defined as dynamical systems that have nonzero Kolmogorov entropy. The hyperbolic dynamical systems that fulfil the Anosov C-condition belong to the MCDS insofar as they have exponential instability of their phase trajectories and positive Kolmogorov entropy. It follows that the C-condition defines a rich class of MCDS that span over an open set in the space of all dynamical systems. The large class of Anosov-Kolmogorov MCDS is realised on Riemannian manifolds of negative sectional curvatures and on high-dimensional tori. The interest in MCDS is rooted in the attempts to understand the relaxation phenomena, the foundations of the statistical mechanics, the appearance of turbulence in fluid dynamics, the non-linear dynamics of Yang-Mills field and gravitating N-body systems as well as black hole thermodynamics. Our aim is to investigate classical-and quantum-mechanical properties of MCDS and their role in the theory of fundamental interactions.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Maximally Chaotic Dynamical Systems and Fundamental Interactions

Savvidy

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…is process is neither periodic nor convergent and is sensitive to the initial value. According to the properties of the dynamical system, chaos can be divided into four types: temporal chaos, spatial chaos, spatiotemporal chaos, and functional chaos [1][2][3][4][5]. e application of chaos can be divided into chaos synthesis and chaos analysis [5].…”

Section: Introductionmentioning

confidence: 99%

Generating Chaotic Series via Encryption Method in Fractional-Order Chua Systems

Gong

Zhang

Wan

2021

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

Fractional-order Chua systems have drawn wide attention in view of rich dynamic characteristics, e.g., chaos and hyperchaos. How to generate chaotic series via encryption method in fractional-order Chua systems is a difficult point all the while. In this paper, we derive several encryption methods in fractional-order Chua systems to generate chaotic series. As one of the most direct application, image encryption is also discussed by the presented methods.

show abstract

“…The existence of chaos of classical homogeneous YM fields has been reported already some time ago [8][9][10][11] but still these YM fields and related models attract attention of researchers (see e.g. [16][17][18]).…”

Section: Introductionmentioning

confidence: 99%

Deconfinement of classical Yang-Mills color fields in a disorder potential

Ermann,

Shepelyansky

2021

Preprint

View full text Add to dashboard Cite

We study numerically and analytically the behavior of classical Yang-Mills color fields in a random one-dimensional potential described by the Anderson model with disorder. Above a certain threshold the nonlinear interactions of Yang-Mills fields lead to chaos and deconfinement of color wavepackets with their subdiffusive spreading in space. The algebraic exponent of the second moment growth in time is found to be in a range of 0.3 to 0.4. Below the threshold color wavepackets remain confined even if a very slow spreading at very long times is not excluded due to subtle nonlinear effects and the Arnold diffusion for the case when initially color packets are located in a close vicinity. In a case of large initial separation of color wavepackets they remain well confined and localized in space. We also present comparison with the behavior of the one-component field model of discrete Anderson nonlinear Schrödinger equation with disorder.

show abstract

Maximally chaotic dynamical systems

Cited by 16 publications

References 83 publications

Maximally Chaotic Dynamical Systems and Fundamental Interactions

Maximally Chaotic Dynamical Systems and Fundamental Interactions

Generating Chaotic Series via Encryption Method in Fractional-Order Chua Systems

Deconfinement of classical Yang-Mills color fields in a disorder potential

Contact Info

Product

Resources

About