Rotation Numbers of Discontinuous Orientation-Preserving Circle Maps

Set-Valued Analysis

Volumn 11, Issue 4, 2003, Pages 359-371

  Brette, Romain ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Circle maps; Discontinuous dynamics; Rotation number; Set valued analysis

Indexed keywords

EID: 1642540984     PISSN: 09276947     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025644532200     Document Type: Article

References (9)

1. Aubin, J. P. and Frankowska, H.: Set-Valued Analysis, Birkhäuser, Basel, 1990.
2. Cornfeld, I. P., Fomin, S. V. and Sinai, Ya. G.: Ergodic Theory, Grundlehren Math. Wiss. 245, Springer-Verlag, Berlin, 1981.
3. Deimling, K.: Multivalued Differential Equations, De Gruyter, Berlin, 1992.
4. Keener, J. P.: Chaotic behavior in piecewise continuous difference equations, Trans. Amer. Math. Soc. 261 (1980), 589-604.
5. Keener, J. P., Hoppensteadt, F. C. and Rinzel, J.: Integrate-and-fire models of nerve membrane response to oscillatory input, SIAM J. Appl. Math. 41 (1981), 503-517.
6. Rhodes, F. and Thompson, C. L.: Rotation numbers for monotone functions on the circle, J. London Math. Soc. 34 (1986), 360-368.
7. Rhodes, F. and Thompson, C. L.: Topologies and rotation numbers for families of monotone functions on the circle, J. London Math. Soc. 43 (1991), 156-170.
8. Rockafellar, R. T. and Wets, R.: Variational Analysis, Springer-Verlag, Berlin, 1997.
9. Rugh, H. H.: Personal communication.