Abstract
An observation of single trajectories exhibiting chaotic motion turns out to be disadvantageous because even smallest variations of the initial conditions grow exponentially in time and result in an unpredictable long-time behaviour. The paper gives a different approach based on a probability distribution of the state space variables which is invariant on the area of attraction and results in a global description of chaotic motion.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Karagiannis, K.Analyse stoßbehafteter Schwingungssysteme mit Anwendung auf Reseelschwingungen beim Zahuradgetriebe, VDI Fortschrittberichte, Reihe 11 Schwingungstechnik, Nr. 125, 1989.
Kunert, A. and Pfeiffer, F., ‘Stochastic model for rattling in gear-boxes’, inProceedings of Nonlinear Dynamics in Engineering Systems, IUTAM Symposium Stuttgart, Germany 1989, W. Schiehlen (ed.), Springer Verlag, Berlin-Heidelberg, 1990.
Kreuzer, E.,Numerische Untersuchung nichtlinearer dynamicscher Systeme, Springer Verlag, Berlin-Heidelberg-New York, 1987.
Pfeiffer, F., ‘Seltsame Attrakteren in Zahnradgetrieben’,Ingenieur-Archiv 58, 1988, 113–125.
Pfeiffer, F. and Kunert, A., ‘Rattling models from deterministic to stochastic processes’,Nonlinear Dynamics,1, 1990, 63–74.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kunert, A., Pfeiffer, F. Description of chaotic motion by an invariant probability density. Nonlinear Dyn 2, 291–304 (1991). https://doi.org/10.1007/BF00045298
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00045298