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 $C^1$ densities if one wishes to determine dynamical obstructions to the
presence of attractors.
Keywords:
invariant measures, attractors, nonholonomic systems, Suslov problem
Citation:
García-Naranjo L. C., Ortega R., Ureña A. J., Invariant Measures as Obstructions to Attractors in Dynamical Systems and Their Role in Nonholonomic Mechanics, Regular and Chaotic Dynamics,
2024, Volume 29, Number 5,
pp. 751-763