Título:
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Periodic orbits in complex Abel equation
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Autor/a:
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Cimà, Anna; Gasull, Armengol; Mañosas Capellades, Francesc; Universitat Autònoma de Barcelona. Centre de Recerca Matemàtica
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Abstract:
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This paper is devoted to prove two unexpected properties of the Abel equation dz/dt = z 3 +B(t)z 2 +C(t)z, where B and C are smooth, 2π−periodic complex valuated functions, t ∈ R and z ∈ C. The first one is that there is no upper bound for its number of isolated 2π−periodic solutions. In contrast, recall that if the functions B and C are real valuated then the number of complex 2π−periodic solutions is at most three. The second property is that there are examples of the above equation with B and C being low degree trigonometric polynomials such that the center variety is formed by infinitely many connected components in the space of coefficients of B and C. This result is also in contrast with the characterization of the center variety for the examples of Abel equations dz/dt = A(t)z 3 + B(t)z 2 studied in the literature, where the center variety is located in a finite number of connected components. |
Materia(s):
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-Equacions abelianes -Cicles límits -Pertorbació (Matemàtica) -Dinàmica combinatòria |
Derechos:
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open access
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https://creativecommons.org/licenses/by-nc-nd/2.5/ |
Tipo de documento:
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Article Prepublicació |
Editor:
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Centre de Recerca Matemàtica
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Compartir:
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Uri:
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https://ddd.uab.cat/record/44203
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