Commenced in January 2007
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Complexity of Multivalued Maps

Authors: David Sherwell, Vivien Visaya


We consider the topological entropy of maps that in general, cannot be described by one-dimensional dynamics. In particular, we show that for a multivalued map F generated by singlevalued maps, the topological entropy of any of the single-value map bounds the topological entropy of F from below.

Keywords: Topological Entropy, Multivalued maps, Selectors

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[1] Alsed`a, J. Llibre, & M. Misiurewicz, Combinatorial Dynamics and Entropy in Dimension One (2nd. ed.), World Scientific, 2000.
[2] A. Baker, Lower bounds on entropy via the Conley index with applications to time series, Topology and Its Applications 120 (2000) 333-354.
[3] S. Day, R. Frongillo, and R. Trevino, Algorithms for Rigorous bound and symbolic dynamics
[4] M. Hurley, On topological entropy of maps, Ergodic Th. & Dynam. Sys. 15 (1995) 557-568.
[5] Z. Nitecki, Preimage entropy for mappings, International Journal of Bifurcation and Chaos 9 (1999) 1815-1843.
[6] C.L. Mberi Kimpolo, Deterministic Dynamics in Questionnaires in the Social Sciences, Ph.D. Thesis, University of the Witwatersrand (2010), Supervisor D. Sherwell.
[7] KS2 C. L. Mberi Kimpolo, D. Sherwell, et al., Orbit Theory: Analysis of Longitudinal Data by Visualization of Fitness States, submitted.
[8] R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. AMS 153 (1971) 509-510.
[9] M. Mrozek, Topological invariants, multivalued maps and computer assisted proofs in dynamics, Computers Math. Applic. 32 (1996) 83-104.
[10] R. Gilmore and M. Lefranc, The Topology of Chaos, John Wiley & Sons. Inc. (2002).
[11] C. Robinson, Dynamical Systems: Stability, Symbolic Dynamics, & Chaos, C.R.C. Press, 1994.