Some characterizations about Siegel curves
Abstract
Let Ψ: ℝ×T ↦ T be a continuous dynamical system on the two-dimensional torus T. The aim of this paper is to prove some characterizations about the existence of a Siegel curve, i.e. a simple closed curve which cuts every half-trajectory of the dynamical system (T,Ψ). This result completes and precises some results obtained in our article [7].
References
1. D.V. Anosov, V.I. Arnold (eds.), Dynamical Systems I, Encyclopedia Math. Sci. vol. 1, Springer-Verlag, 1988.
2. N.P. Bhatia, G.P. Szegoe, Stability Theory of Dynamical Systems, Grundl. Math. Wiss. 161, Springer-Verlag, 1970.
3. I.P. Cornfeld, S.V. Fomin, Y.G. Sinai, Ergodic Theory, Grundl. Math. Wiss. 245, Springer-Verlag, 1982.
4. O. Forster, Riemannsche Flaechen, Heidel. Taschenbuecher, Springer-Verlag, 1977.
5. M. Hmissi, Semi-groupes déterministes, Lect. Notes in Math. 1393, Springer-Verlag, 1989, 135-144.
6. M. Hmissi, Recouvrement parallélisable du plan, Proc. European Conference on Iteration Theory, Lisboa 1991, J.P. Lampreia et al. (eds.), World Scientific, 1992, 136-145.
7. M. Hmissi, M. Sieveking, Sur I'existence des courbes de Siegel, Grazer Math. Ber. 334 (1997), 139-146.
8. C.L. Siegel, Notes on differential equations on the torus, Ann. Math. 46 (1945), 423-428.
2. N.P. Bhatia, G.P. Szegoe, Stability Theory of Dynamical Systems, Grundl. Math. Wiss. 161, Springer-Verlag, 1970.
3. I.P. Cornfeld, S.V. Fomin, Y.G. Sinai, Ergodic Theory, Grundl. Math. Wiss. 245, Springer-Verlag, 1982.
4. O. Forster, Riemannsche Flaechen, Heidel. Taschenbuecher, Springer-Verlag, 1977.
5. M. Hmissi, Semi-groupes déterministes, Lect. Notes in Math. 1393, Springer-Verlag, 1989, 135-144.
6. M. Hmissi, Recouvrement parallélisable du plan, Proc. European Conference on Iteration Theory, Lisboa 1991, J.P. Lampreia et al. (eds.), World Scientific, 1992, 136-145.
7. M. Hmissi, M. Sieveking, Sur I'existence des courbes de Siegel, Grazer Math. Ber. 334 (1997), 139-146.
8. C.L. Siegel, Notes on differential equations on the torus, Ann. Math. 46 (1945), 423-428.
HmissiM. (1999). Some characterizations about Siegel curves. Annales Mathematicae Silesianae, 13, 143-148. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/14144
Mohamed Hmissi
med.hmissi@fst.rnu.tn
Département de Mathématiques, Faculté des Sciences de Tunis, Tunisia Tunisia
Département de Mathématiques, Faculté des Sciences de Tunis, Tunisia Tunisia
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