Abstract
We introduce the notion of conductance in discrete dynamical systems defined by iterated maps of the interval. Our starting point is the notion of conductance in the graph theory. We pretend to apply the known results in this new context.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Walters, P., ‘An introduction to ergodic theory’, inGraduate Texts in Mathematics, Vol. 79, Springer-Verlag, New York-Berlin, 1982.
Milnor, J. and Thurston, W., ‘On iterated maps of the interval’, inProceedings of the Univ. Maryland 1986–1987, Vol. 1342, J. C. Alexander (ed.), Lect. Notes in Math., Springer-Verlag, Berlin, 1988, pp. 465–563.
Bollobás, B., ‘Modern graph theory’, inGraduate Texts in Mathematics, Vol. 184, Springer-Verlag, New York, 1998.
Mohar, B.,Some Applications of Laplace Eigenvalues of Graphs, Vol. 35, University of Ljubbljana, Preprint series, 1997.
Cannon, J. W. and Wagreich, Ph., ‘Growth functions of surface groups’, Mathematische Annalen 293(2), 1992, 239–257.
Fernandes, S. and Sousa Ramos, J., ‘Spectral invariants and conductance in iterated maps’, in Proceedings of the European Conference on Iteration Theory, ECIT2004, Batschuns, Austria, 29 August – 4 September 2004. Submitted for publication.
Fernandes, S. and Sousa Ramos, J., ‘Spectral invariants of iterated maps of the interval’, Grazer Mathematische Berichte 346, 2004, 113–122.
Fernandes, S. and Sousa Ramos, J., ‘Second smaller zero of kneading’, in Proceedings of the 8th International Conference on Difference Equations and Applications, Brno, Czech Republic, 28 July – 1 August 2003.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fernandes, S., Ramos, J.S. Conductance, Laplacian and Mixing Rate in Discrete Dynamical Systems. Nonlinear Dyn 44, 117–126 (2006). https://doi.org/10.1007/s11071-006-1954-0
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11071-006-1954-0