Premium
Bounds on the Ljapunov Exponent
Author(s) -
Endrullis M.,
Englisch H.
Publication year - 1984
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19844960411
Subject(s) - exponent , physics , statistical physics , operator (biology) , mathematical physics , characterization (materials science) , energy (signal processing) , pure mathematics , quantum mechanics , mathematics , optics , philosophy , linguistics , repressor , transcription factor , gene , biochemistry , chemistry
We present a pedagogical model where the strict positivity of the largest Ljapunov exponent is easily derivable and the exponent can be calculated explicitly. Further, we prove an inequality concerning the Ljapunov exponents of k ‐forms and compare the Ljapunov exponent of a one‐dimensional Schrödinger operator, corresponding to a random substitutional alloy, with those of the attached periodic Hamiltonians, yielding a new characterization for the possible energy levels in this model.