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arXiv.org e-Print Archive
Preprint . 1998
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Communications in Mathematical Physics
Article . 1999 . Peer-reviewed
License: Springer TDM
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https://dx.doi.org/10.48550/ar...
Article . 1998
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Algebraic Entropy

Algebraic entropy
descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jul 1999Embargo end date: 01 Jan 1998Publisher:Springer Science and Business Media LLCJournal:Communications in Mathematical Physics, volume 204, pages 425-437 (issn: 0010-3616, eissn: 1432-0916, Copyright policy )
Authors: Bellon, M. P.; Viallet, C.-M.;

doi: 10.1007/s002200050652 , 10.48550/arxiv.chao-dyn/9805006

arXiv: chao-dyn/9805006

Algebraic Entropy

Abstract

For any discrete time dynamical system with a rational evolution, we define an entropy, which is a global index of complexity for the evolution map. We analyze its basic properties and its relations to the singularities and the irreversibility of the map. We indicate how it can be exactly calculated.

Latex, 12 pages, 1 figure

Related Organizations
Keywords

algebraic entropy, Nonlinear Sciences - Exactly Solvable and Integrable Systems, FOS: Physical sciences, Mathematical Physics (math-ph), Nonlinear Sciences - Chaotic Dynamics, real projective spaces, Discrete version of topics in analysis, Entropy and other invariants, isomorphism, classification in ergodic theory, Chaotic Dynamics (nlin.CD), Exactly Solvable and Integrable Systems (nlin.SI), homogeneous rational mappings, Mathematical Physics

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    Impact byBIP!
    selected citations
    These citations are derived from selected sources.
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 178
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Top 1%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Top 10%
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
178
Top 10%
Top 1%
Top 10%
Green