Temporal scaling at Feigenbaum points and non-extensive thermodynamics

Abstract

We show that recent claims for the non-stationary behaviour of the logistic map at the Feigenbaum point based on non-extensive thermodynamics are either wrong or can be easily deduced from well-known properties of the Feigenbaum attractor. In particular, there is no generalized Pesin identity for this system, the existing "proofs" being based on misconceptions about basic notions of ergodic theory. In deriving several new scaling laws of the Feigenbaum attractor, thorough use is made of its detailed structure, but there is no obvious connection to non-extensive thermodynamics.

arXiv commentaccepted for Phys. Rev. Lett

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Cited by in corpus (13)

• Pesin-Type Identity for Weak Chaos
• Ergodicity Breaking in a Deterministic Dynamical System
• Incidence of nonextensive thermodynamics in temporal scaling at Feigenbaum points
• q-Deformed Statistical-Mechanical Property in the Dynamics of Trajectories en route to the Feigenbaum Attractor
• Dynamics towards the Feigenbaum attractor
• The production of Tsallis entropy in the limit of weak chaos and a new indicator of chaoticity
• Separation of trajectories and its Relation to Entropy for Intermittent Systems with a Zero Lyapunov exponent
• Questioning the validity of non-extensive thermodynamics for classical Hamiltonian systems
• Generalization of the possible algebraic basis of $q$-triplets
• Pesin-type relation for subexponential instability
• Emergent statistical-mechanical structure in the dynamics along the period-doubling route to chaos
• Numerical estimate of infinite invariant densities: application to Pesin-type identity
• Routes to chaos, universality and glass formation