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2015 | OriginalPaper | Chapter

Discrete Symmetric Planar Dynamics

Authors : B. Alarcón, S. B. S. D. Castro, I. S. Labouriau

Published in: Dynamics, Games and Science

Publisher: Springer International Publishing

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Abstract

We review previous results providing sufficient conditions to determine the global dynamics for equivariant maps of the plane with a unique fixed point which is also hyperbolic.

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Literature
1.
go back to reference Alarcón, B.: Rotation numbers for planar attractors of equivariant homeomorphisms. Topological Methods Nonlinear Anal. 42(2), 327–343 (2013)MATH Alarcón, B.: Rotation numbers for planar attractors of equivariant homeomorphisms. Topological Methods Nonlinear Anal. 42(2), 327–343 (2013)MATH
2.
go back to reference Alarcón, B., Castro, S.B.S.D., Labouriau, I.S.: A local but not global attractor for a Z n -symmetric map. J. Singularities 6, 1–14 (2012)MATH Alarcón, B., Castro, S.B.S.D., Labouriau, I.S.: A local but not global attractor for a Z n -symmetric map. J. Singularities 6, 1–14 (2012)MATH
3.
go back to reference Alarcón, B., Castro, S.B.S.D., Labouriau, I.S.: The discrete Markus-Yamabe problem for symmetric planar polynomial maps. Indag. Math. 23, 603–608 (2012)MathSciNetCrossRefMATH Alarcón, B., Castro, S.B.S.D., Labouriau, I.S.: The discrete Markus-Yamabe problem for symmetric planar polynomial maps. Indag. Math. 23, 603–608 (2012)MathSciNetCrossRefMATH
4.
go back to reference Alarcón, B., Castro, S.B.S.D., Labouriau, I.S.: Global dynamics for symmetric planar maps. Discrete Contin. Dyn. Syst. A 37, 2241–2251 (2013) Alarcón, B., Castro, S.B.S.D., Labouriau, I.S.: Global dynamics for symmetric planar maps. Discrete Contin. Dyn. Syst. A 37, 2241–2251 (2013)
5.
go back to reference Alarcón, B., Castro, S.B.S.D., Labouriau, I.S.: Global saddle for planar diffeomorphisms (in preparation) Alarcón, B., Castro, S.B.S.D., Labouriau, I.S.: Global saddle for planar diffeomorphisms (in preparation)
6.
go back to reference Alarcón, B., Guíñez, V., Gutierrez, C.: Planar embeddings with a globally attracting fixed point. Nonlinear Anal. 69(1), 140–150 (2008)MathSciNetCrossRefMATH Alarcón, B., Guíñez, V., Gutierrez, C.: Planar embeddings with a globally attracting fixed point. Nonlinear Anal. 69(1), 140–150 (2008)MathSciNetCrossRefMATH
7.
go back to reference Bhatia, N.P., Szegö, G.P.: Stability Theory of Dynamical Systems. Springer, New York (2002)MATH Bhatia, N.P., Szegö, G.P.: Stability Theory of Dynamical Systems. Springer, New York (2002)MATH
8.
go back to reference Cima, A., van den Essen, A., Gasull, A., Hubbers, E., Mañosas, F.: A polynomial couterexample to the Markus-Yamabe conjecture. Adv. Math. 131, 453–457 (1997)MathSciNetCrossRefMATH Cima, A., van den Essen, A., Gasull, A., Hubbers, E., Mañosas, F.: A polynomial couterexample to the Markus-Yamabe conjecture. Adv. Math. 131, 453–457 (1997)MathSciNetCrossRefMATH
10.
go back to reference Golubitsky, M., Stewart, I., Schaeffer, D.G.: Singularities and Groups in Bifurcation Theory, Vol. 2. Applied Mathematical Sciences, vol. 69. Springer, New York (1985) Golubitsky, M., Stewart, I., Schaeffer, D.G.: Singularities and Groups in Bifurcation Theory, Vol. 2. Applied Mathematical Sciences, vol. 69. Springer, New York (1985)
11.
go back to reference Hernández-Corbato, L., Ortega, R., Ruiz del Portal, F.R.: Attractors with irrational rotation number. Math. Proc. Camb. Philos. Soc. 153, 59–77 (201) Hernández-Corbato, L., Ortega, R., Ruiz del Portal, F.R.: Attractors with irrational rotation number. Math. Proc. Camb. Philos. Soc. 153, 59–77 (201)
13.
Metadata
Title
Discrete Symmetric Planar Dynamics
Authors
B. Alarcón
S. B. S. D. Castro
I. S. Labouriau
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-16118-1_2

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