Routes to chaos, universality and glass formation

Fulvio Baldovin

Physica A: Statistical Mechanics and its Applications, 2006, vol. 372, issue 2, 224-237

Abstract: We review recent results obtained for the dynamics of incipient chaos. These results suggest a common picture underlying the three universal routes to chaos displayed by the prototypical logistic and circle maps. Namely, the period doubling, intermittency, and quasiperiodicity routes. In these situations the dynamical behavior is exactly describable through infinite families of Tsallis’q-exponential functions. Furthermore, the addition of a noise perturbation to the dynamics at the onset of chaos of the logistic map allows to establish parallels with the behavior of supercooled liquids close to glass formation. Specifically, the occurrence of two-step relaxation, aging with its characteristic scaling property, and subdiffusion and arrest is corroborated for such a system.

Keywords: Nonlinear dynamics; Renormalization group; Weak chaos; Glass formation (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:372:y:2006:i:2:p:224-237

DOI: 10.1016/j.physa.2006.08.057

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