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Convective Lyapunov Spectra (Articolo in rivista)

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Aurélien Kenfack Jiotsa (1,2); Antonio Politi (2,3); Alessandro Torcini (2,4,5) (2013)
Convective Lyapunov Spectra
in Journal of physics. A, Mathematical and theoretical (Print); IOP PUBLISHING, BRISTOL (Regno Unito)
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Aurélien Kenfack Jiotsa (1,2); Antonio Politi (2,3); Alessandro Torcini (2,4,5) (literal)

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This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Lyapunov analysis: from dynamical systems theory to applications'. (literal)

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(1) Département de Physique, Ecole Normale Supérieure, Université de Yaoundé I, BP 42 Yaoundé, Cameroon (2) Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy (3) Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom (4) Centro Interdipartimentale per lo Studio delle Dinamiche Complesse, via Sansone 1, I-50019 Sesto Fiorentino, Italy (5) INFN Sez. Firenze, via Sansone 1, I-50019 Sesto Fiorentino, Italy (literal)

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Abstract

We generalize the concept of the convective (or velocity-dependent) Lyapunov exponent from the maximum rate Lambda (v) to an entire spectrum Lambda (v, n). Our results are derived by following two distinct computational protocols: (i) Legendre transform within the chronotopic approach (Lepri et al 1996 J. Stat. Phys. 82 1429); (ii) by letting evolve an ensemble of initially localized perturbations. The two approaches turn out to be mutually consistent. Moreover, we find the existence of a phase transition: above a critical value n = n(c) of the integrated density of exponents, the zero-velocity convective exponent is strictly smaller than the corresponding Lyapunov exponent. This phenomenon is traced back to a change of concavity of the so-called temporal Lyapunov spectrum for n > n(c), which, therefore, turns out to be a dynamically invariant quantity. (literal)

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