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A Skew Product Entropy for Nonsingular Transformations
Author(s) -
Silva Cesar E.,
Thieullen Philippe
Publication year - 1995
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/52.3.497
Subject(s) - skew , invertible matrix , mathematics , automorphism , entropy (arrow of time) , pure mathematics , ternary operation , physics , computer science , thermodynamics , programming language , astronomy
We define a skew product entropy for conservative nonsingular transformations, show that it takes values in {0, ∞} and use it to distinguish two classes on nonsingular transformations. Binary and ternary type III λ odometers have zero skew product entropy, while nonsingular K‐automorphisms have infinite skew product entropy.