Dynamical Systems on Monoids: Toward a General Theory of Deterministic System and Motion

Mazzola, Claudio and Giunti, Marco (2012). Dynamical Systems on Monoids: Toward a General Theory of Deterministic System and Motion. In Gianfranco Minati, Mario Abram and Eliano Pessa (Ed.), Methods, Models, Simulations and Approaches Towards a General Theory of Change (pp. 173-185) Singapore: World Scientific. doi:10.1142/9789814383332_0012


Author Mazzola, Claudio
Giunti, Marco
Title of chapter Dynamical Systems on Monoids: Toward a General Theory of Deterministic System and Motion
Title of book Methods, Models, Simulations and Approaches Towards a General Theory of Change
Place of Publication Singapore
Publisher World Scientific
Publication Year 2012
Sub-type Research book chapter (original research)
DOI 10.1142/9789814383332_0012
Open Access Status
Year available 2012
ISBN 9789814383325
9789814452960
9789814383332
Editor Gianfranco Minati
Mario Abram
Eliano Pessa
Start page 173
End page 185
Collection year 2013
Language eng
Formatted Abstract/Summary
 Dynamical systems are mathematical structures whose aim is to describe the evolution of an arbitrary deterministic system through time, which is typically modeled as (a subset of) the integers or the real numbers. We show that it is possible to generalize the standard notion of a dynamical system, so that its time dimension is only required to possess the algebraic structure of a monoid: first, we endow any dynamical system with an associated graph and, second, we prove that such a graph is a category if and only if the time model of the dynamical system is a monoid. In addition, we show that the general notion of a dynamical system allows us not only to define a family of meaningful dynamical concepts, but also to distinguish among a cluster of otherwise tangled notions of reversibility, whose logical relationships are finally analyzed.
Keyword Dynamical System
Reversibility
Irreversibility
Category Theory
Q-Index Code B1
Q-Index Status Provisional Code
Institutional Status Non-UQ
Additional Notes Proceedings of the Fifth National Conference of the Italian Systems Society Marche Polytechnic University, Italy, 14 – 16 October 2010

Document type: Book Chapter
Collection: School of Historical and Philosophical Inquiry
 
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Created: Fri, 01 Aug 2014, 17:09:54 EST by Claudio Mazzola on behalf of School of Historical and Philosophical Inquiry