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Volume 5, Issue 1 (2015), Pages [1] - [67]
ON THE REGULARITY OF THE DISPLACEMENT SEQUENCE OF AN ORIENTATION PRESERVING CIRCLE HOMEOMORPHISM
[1] V. I. Arnol’d, Cardiac arrhythmias and circle maps, Chaos 1 (1991), 20-24.
[2] I. D. Berg and A. Wilansky, Periodic, almost-periodic, and semiperiodic sequences, Michigan Math. J. 9 (1962), 363-368.
[3] R. Brette, Dynamics of one-dimensional spiking neuron model, J. Math. Biol. 48 (2004), 38-56.
[4] H. Carrillo and F. Hoppensteadt, Unfolding an electronic integrate-and-fire circuit, Biol. Cybern. 102 (2010), 1-8.
[5] S. Coombes and P. Bressloff, Mode locking and
[6] G. Craciun, P. Horja, M. Prunescu and T. Zamfirescu, Most homeomorphisms of the circle are semiperiodic, Arch. Math. 64 (1995), 452-458.
[7] W. de Melo and S. van Strien, One-Dimensional Dynamics,
[8] T. Gedeon and M. Holzer, Phase locking in integrate-and-fire models with refractory periods and modulation, J. Math. Biol. 49 (2004), 577-603.
[9] W. H. Gottschalk, Minimal sets: An introduction to topological dynamics, Bull. Amer. Math. So. 64 (1958), 336-351.
[10] J. P. Keener, F. C. Hoppensteadt and J. Rinzel, Integrate-and-fire models of nerve membrane response to oscillatory input, SIAM J. Appl. Math 41 (1981), 503-517.
[11] A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Encyclopedia of Mathematics and its Applications (No. 54), Cambridge University Press, 1995.
[12] W. Marzantowicz and J. Signerska, Firing map of an almost periodic input function, DCDS Suppl. 2011(2) (2011), 1032-1041.
[13] W. Marzantowicz and J. Signerska, Distribution of the displacement sequence of an orientation preserving circle homeomorphism, Dyn. Syst. 29 (2014), 153-166.