The Multifractal Time and Irreversibility in Dynamic Systems

2000/02/01 by L. Ya. Kobelev, Kobelev, L. Ya. · 2 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Classical Physics (physics.class-ph) #Complex Systems and Dynamics #Complex Systems and Time Series Analysis #FOS: Physical sciences #General Physics (physics.gen-ph) #advanced mathematical theories #physics.class-ph #physics.gen-ph

paper · pdf · doi:10.48550/arxiv.physics/0002002

RevTeX

arxiv created 2000/02/01 · openalex publication_date 2000/02/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The irreversibility of the equations of classical dynamics (the Hamilton equations and the Liouville equation) in the space with multifractal time is demonstrated. The time is given on multifractal sets with fractional dimensions. The last depends on densities of Lagrangians in a given time moment and in a given point of space. After transition to sets of time points with the integer dimension the obtained equations transfer in the known equations of classical dynamics. Production of an entropy is not equally to zero in space with multifractal time, i.e. the classical systems in this space are non-closed.

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• The Theory of Gravitation in the Space - Time with Fractal Dimensions and Modified Lorents Transformations
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