Commenced in January 2007
Paper Count: 30840
Complexity of Multivalued Maps
Abstract: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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1330421Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 841
 Alsed`a, J. Llibre, & M. Misiurewicz, Combinatorial Dynamics and Entropy in Dimension One (2nd. ed.), World Scientific, 2000.
 A. Baker, Lower bounds on entropy via the Conley index with applications to time series, Topology and Its Applications 120 (2000) 333-354.
 S. Day, R. Frongillo, and R. Trevino, Algorithms for Rigorous bound and symbolic dynamics
 M. Hurley, On topological entropy of maps, Ergodic Th. & Dynam. Sys. 15 (1995) 557-568.
 Z. Nitecki, Preimage entropy for mappings, International Journal of Bifurcation and Chaos 9 (1999) 1815-1843.
 C.L. Mberi Kimpolo, Deterministic Dynamics in Questionnaires in the Social Sciences, Ph.D. Thesis, University of the Witwatersrand (2010), Supervisor D. Sherwell.
 KS2 C. L. Mberi Kimpolo, D. Sherwell, et al., Orbit Theory: Analysis of Longitudinal Data by Visualization of Fitness States, submitted.
 R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. AMS 153 (1971) 509-510.
 M. Mrozek, Topological invariants, multivalued maps and computer assisted proofs in dynamics, Computers Math. Applic. 32 (1996) 83-104.
 R. Gilmore and M. Lefranc, The Topology of Chaos, John Wiley & Sons. Inc. (2002).
 C. Robinson, Dynamical Systems: Stability, Symbolic Dynamics, & Chaos, C.R.C. Press, 1994.