Why Instantaneous Values of the “Covariant” Lyapunov Exponents Depend upon the Chosen State-Space Scale

• Autorzy: Hoover W. G. , Hoover C. G.

Identyfikatory

DOI

10.12921/cmst.2014.20.01.5-8

• Języki publikacji: EN

Abstrakty

EN

We explore a simple example of a chaotic thermostated harmonic-oscillator system which exhibits qualitatively different local Lyapunov exponents for simple scale-model constant-volume transformations of its coordinate q and momentum p: {q, p} ! {(Q/s), (sP)}. The time-dependent thermostat variable ζ(t) is unchanged by such scaling. The original (qpζ) motion and the scale-model (QPζ) version of the motion are physically identical. But both the local Gram-Schmidt Lyapunov exponents and the related local “covariant” exponents change with the change of scale. Thus this model furnishes a clearcut chaotic time-reversible example showing how and why both the local Lyapunov exponents and covariant exponents vary with the scale factor s.

Słowa kluczowe

EN

Lyapunov instability; thermostats; chaotic dynamics

• Wydawca: Institute of Bioorganic Chemistry Scientific Publishers OWN, Polish Academy of Sciences
• Czasopismo: Computational Methods in Science and Technology
• Rocznik: 2014
• Tom: Vol. 20, No. 1
• Strony: 5--8
• Opis fizyczny: Bibliogr. 15 poz., rys.

Twórcy

autor

Hoover W. G.

• Ruby Valley Research Institute Highway Contract 60, Box 601 Ruby Valley, Nevada 89833

autor

Hoover C. G.

• Ruby Valley Research Institute Highway Contract 60, Box 601 Ruby Valley, Nevada 89833

Bibliografia

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• [2] H.A. Posch, Symmetry Properties of Orthogonal and Covariant Lyapunov Vectors and Their Exponents, arXiv:1107.4032 (2012); Journal of Physics A: Mathematical and Theoretical 46, 254006 (2013).
• [3] H-L. Yang and G. Radons, Comparison between Covariant and Orthogonal Lyapunov Vectors, Physical Review E 82, 046204 (2010).
• [4] F. Ginelli, P. Poggi, A. Turchi, H. Chaté, R. Livi, and A. Politi, Characterizing Dynamics with Covariant Lyapunov Vectors Physical Review Letters 99, 130601 (2007).
• [5] M. Romero-Bastida, D. Pazó, J.M. López, and M.A. Rodríguez, Structure of Characteristic Lyapunov Vectors in Anharmonic Hamiltonian Lattices, Physical Review E 82, 036205 (2010).
• [6] C.L. Wolfe and R.M. Samelson. An Efficient Method for Recovering Lyapunov Vectors from Singular Vectors, Tellus 59A, 355-366 (2007).
• [7] W.G. Hoover and H.A. Posch, Direct Measurement of Lyapunov Exponents, Physics Letters A 113, 82-84 (1985).
• [8] Wm.G. Hoover and C.G. Hoover, Local Gram-Schmidt and Covariant Lyapunov Vectors and Exponents for Three Harmonic Oscillator Problems, Communications in Nonlinear Science and Numerical Simulation 17, 1043-1054 (2012).
• [9] Wm.G. Hoover, C.G. Hoover, and H.A. Posch, Lyapunov Instability of Pendulums, Chains, and Strings, Physical Review A 41, 2999-3004 (1990).
• [10] H.A. Posch and Wm.G. Hoover, Time-Reversible Dissipative Attractors in Three and Four Phase-Space Dimensions, Physical Review E 55, 6803-6810 (1997).
• [11] Wm.G. Hoover, Canonical Dynamics: Equilibrium Phase-Space Distributions, Physical Review A 31, 1695-97 (1985).
• [12] H.A. Posch, Wm.G. Hoover, and F.J. Vesely, Canonical Dynamics of the Nosé Oscillator: Stability, Order, and Chaos, Physical Review A 33, 4253-4265 (1986).
• [13] Wm.G. Hoover, Remark on ‘Some Simple Chaotic Flows’, Physical Review E 51, 759-760 (1995).
• [14] J.C. Sprott, Some Simple Chaotic Flows, Physical Review E 50, R647-R650 (1994).
• [15] Wm.G. Hoover and C.G. Hoover, Time-Symmetry Breaking in Hamiltonian Mechanics, arXiv 1302.2533 (2013); Computational Methods in Science and Technology 19, 77-87 (2013).