Temporal scaling at feigenbaum points and nonextensive thermodynamics

被引：27

作者：

Grassberger, P ^{[1
]}

机构：

[1] Forschungszentrum Julich, John Von Neumann Inst Comp, D-52425 Julich, Germany

[2] Perimeter Inst Theoret Phys, Waterloo, ON N2L 2Y5, Canada

来源：

PHYSICAL REVIEW LETTERS | 2005年 / 95卷 / 14期

关键词：

D O I：

10.1103/PhysRevLett.95.140601

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We show that recent claims for the nonstationary behavior of the logistic map at the Feigenbaum point based on nonextensive thermodynamics are either incorrect 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 attempts at 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 nonextensive thermodynamics.

引用

页数：4

共 35 条

[1] DYNAMICAL BEHAVIOR AT THE ONSET OF CHAOS [J].

ANANIA, G ;

POLITI, A .

EUROPHYSICS LETTERS, 1988, 7 (02) :119-124

[2] Ensemble averages and nonextensivity at the edge of chaos of one-dimensional maps -: art. no. 020601 [J].

Añaños, GFJ ;

Tsallis, C .

PHYSICAL REVIEW LETTERS, 2004, 93 (02) :020601-1

[3]

[Anonymous], 2012, Probability Theory: The Logic Of Science

[4] Nonextensive Pesin identity: Exact renormalization group analytical results for the dynamics at the edge of chaos of the logistic map [J].

Baldovin, F ;

Robledo, A .

PHYSICAL REVIEW E, 2004, 69 (04) :4-1

[5]

Baldovin F, 2002, PHYS REV E, V66, DOI [10.1103/PhysRevE.66.045104, 10.1103/PhysrevE.66.045104]

[6] Sensitivity to initial conditions at bifurcations in one-dimensional nonlinear maps: Rigorous nonextensive solutions [J].

Baldovin, F ;

Robledo, A .

EUROPHYSICS LETTERS, 2002, 60 (04) :518-524

[7] Nonequilibrium probabilistic dynamics of the logistic map at the edge of chaos -: art. no. 254103 [J].

Borges, EP ;

Tsallis, C ;

Añaños, GFJ ;

de Oliveira, PMC .

PHYSICAL REVIEW LETTERS, 2002, 89 (25)

[8] A non extensive approach to the entropy of symbolic sequences [J].

Buiatti, M ;

Grigolini, P ;

Palatella, L .

PHYSICA A, 1999, 268 (1-2) :214-224

[9] Weak insensitivity to initial conditions at the edge of chaos in the logistic map [J].

Coraddu, M ;

Meloni, F ;

Mezzorani, G ;

Tonelli, R .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2004, 340 (1-3) :234-239

[10] Power-law sensitivity to initial conditions within a logisticlike family of maps: Fractality and nonextensivity [J].

Costa, UMS ;

Lyra, ML ;

Plastino, AR ;

Tsallis, C .

PHYSICAL REVIEW E, 1997, 56 (01) :245-250

← 1 2 3 4 →