Abstract:
We present some results on the absence of a wide class of invariant measures for
dynamical systems possessing attractors. We then consider a generalization of the classical
nonholonomic Suslov problem which shows how previous investigations of existence of invariant
measures for nonholonomic systems should necessarily be extended beyond the class of measures
with strictly positive C1C1 densities if one wishes to determine dynamical obstructions to the
presence of attractors.
Keywords:
invariant measures, attractors, nonholonomic systems, Suslov problem
LGN acknowledges support from the project MIUR-PRIN 2022FPZEES Stability in Hamiltonian
dynamics and beyond. RO and AU acknowledge funding provided by the Spanish MICINN
project PID2021-128418NA-I00.
Received: 23.04.2024 Accepted: 24.07.2024
Document Type:
Article
Language: English
Citation:
Luis C. García-Naranjo, Rafael Ortega, Antonio J. Ureña, “Invariant Measures as Obstructions to Attractors in Dynamical Systems and Their Role in Nonholonomic Mechanics”, Regul. Chaotic Dyn., 29:5 (2024), 751–763
\Bibitem{GarOrtUre24}
\by Luis C. Garc{\'\i}a-Naranjo, Rafael Ortega, Antonio J. Ure\~na
\paper Invariant Measures as Obstructions to Attractors in Dynamical Systems and Their Role in Nonholonomic Mechanics
\jour Regul. Chaotic Dyn.
\yr 2024
\vol 29
\issue 5
\pages 751--763
\mathnet{http://mi.mathnet.ru/rcd1279}
\crossref{https://doi.org/10.1134/S156035472456003X}
Linking options:
https://www.mathnet.ru/eng/rcd1279
https://www.mathnet.ru/eng/rcd/v29/i5/p751
This publication is cited in the following 1 articles:
Mariana Costa-Villegas, Luis C. García-Naranjo, “Affine Generalizations of the Nonholonomic Problem of a Convex Body Rolling without Slipping on the Plane”, Regul. Chaot. Dyn., 2025
Citation in format AMSBIB
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