Abstract
This work considers reversed evolution in dynamical systems. In particular, asymptotic behavior of chaotic systems, when their orbits evolve backward in time. Reversed dynamics reveals important aspects of the trajectories, such as a new necessary parameter. This is the strategy through which one orbit reaches an original state in the past. As a result, it is found that backward orbits exhibit sensitivity to the strategy. This gives additional evidence about the unpredictability of the past.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Barnsley, M.F., Demko, S.: Iterated function systems and the global construction of fractals. Proc. R. Soc. Lond. A399, 243–275 (1985).
Bennett, R.: On Inverse Limit Sequences, Master’s thesis, University of Tennessee (1962).
Davis, J.F.: Confluent mappings on \([0, 1]\) and inverse limits. Topol. Proc. 15, 1–9 (1990).
Gardini, L., Hommes, C., Tramontanac, F., de Vilderd, R.: Forward and backward dynamics in implicitly defined overlapping generations models. J. Econ. Behav. Organ. 71, 110–129 (2009).
Ingram, W.T.: Invariant sets and inverse limits. Topol. Appl. 126, 393–408 (2002).
Kennedy, J., Stockman, D. R., Yorke, J.A.: Inverse limits and an implicitly defined difference equation from economics. Topol. Appl. 154, 2533–2552 (2007).
Kyrtsou, C., Vorlow, C.: Complex dynamics in macroeconomics: a novel approach. In: Diebolt, C., Kyrtsou, C. (eds.) New Trends In Macroeconomics, pp. 223–245, Springer-Verlag, Berlin (2005).
Laplace, P.S.: Traité de Mécanique Céleste. Oeuvres complètes, Vol. 5, Gauthier-Villars, Paris (1825).
Lorenz, E.N.: Deterministic non-periodic flow. J. Atmos. Sci. 20, 130–141 (1963).
May, R.M., McLean, A.R.: Theoretical Ecology: Principles and Applications. Blackwell, Oxford (2007).
Medio, A., Raines, B.E.: Inverse limit spaces arising from problems in economics. Topol. Appl. 153, 3437–3449 (2006).
Mira, C., Gardini L., Barugola, A., Cathala, J.-C.: Chaotic Dynamics in Two-Dimensional Noninvertible Maps. Series A, 20. World Scientific Publishing, Singapore (1996).
Pellicer-Lostao, C., López-Ruiz, R.: A chaotic gas-like model for trading markets. J. Comput. Sci. 1, 24–32 (2010).
Poincaré, H.: Les méthodes Nouvelles de la Mécanique Céleste, 3 volumes. Gauthiers-Villars, Paris (1892).
Bergé, P., Pomeau, Y., Vidal, C.: L’Ordre dans le Chaos. Hermann, Paris (1984).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Pellicer-Lostao, C., López-Ruiz, R. (2015). The Importance of the Strategy in Backward Orbits. In: López-Ruiz, R., Fournier-Prunaret, D., Nishio, Y., Grácio, C. (eds) Nonlinear Maps and their Applications. Springer Proceedings in Mathematics & Statistics, vol 112. Springer, Cham. https://doi.org/10.1007/978-3-319-12328-8_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-12328-8_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12327-1
Online ISBN: 978-3-319-12328-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)