1996/02/28 by Federico Bonetto, F. Bonetto, G. Gallavotti +1 · 56 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Attractor #Axiom #Chaotic #Computer science #Epistemology #Geometry #Granularity #Invariance principle #Mathematical analysis #Mathematics #Origins and Evolution of Life #Philosophy #Physics #Property (philosophy) #Pure mathematics #Quantum Mechanics and Applications #Statistical physics #Symmetry (geometry) #Theoretical physics #chao-dyn #nlin.CD
paper · pdf · doi:10.1007/s002200050200
published in Communications in Mathematical Physics 189(2), 263-275 (Springer Science+Business Media) · 15 pages, plain TeX, no figures
arxiv created 1996/02/28 · openalex publication_date 1997/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We describe a way of interpreting the chaotic principle of (ref. [GC1]) more extensively than it was meant in the original works. Mathematically the analysis is based on the dynamical notions of Axiom A and Axiom B and on the notion of Axiom C, that we introduce arguing that it is suggested by the results of an experiment (ref. [BGG]) on chaotic motions. Physically we interpret a breakdown of the Anosov property of a time reversible attractor (replaced, as a control parameter changes, by an Axiom A property) as a spontaneous breakdown of the time reversal symmetry: the relation between time reversal and the symmetry that remains after the breakdown is analogous to the breakdown of T-invariance while TCP still holds.