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CHAOTIC POLYNOMIALS IN SPACES OF CONTINUOUS AND DIFFERENTIABLE FUNCTIONS

Published online by Cambridge University Press:  01 May 2008

RICHARD M. ARON
Affiliation:
Department of Mathematics, Kent State University Kent, OH 44240U.S.A. e-mail: aron@math.kent.edu
ALEJANDRO MIRALLES
Affiliation:
Departamento de Análisis Matemático Av/ Dr. Moliner, 50 Burjassot 46100Spain e-mail: alejandro.miralles@uv.es
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Abstract

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We construct chaotic m-homogeneous maps acting on for any m ≥ 2, and on the Fréchet spaces for odd values of m ≥ 3 and for any m ≥ 2.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Bernardes, N.. On orbits of polynomial maps in Banach spaces, South African Math. Soc. 21 (1998), 311318.Google Scholar
2.Birkhoff, G.Démonstration d'un théoréme elémentaire sur les fonctions entiéres, C. R. Acad. Sci. Paris 189 (1929), 473475.Google Scholar
3.Giménez, F. Martínez, Universalidad, hiperciclicidad, y caos en espacios de Fréchet, Thesis (Universidad Politécnica de Valencia 2000).Google Scholar
4.Peris, A.Chaotic polynomials on fréchet spaces, Proc. Amer. Math. Soc. 127 (1999), 36013603; Erratum to Chaotic polynomials on fréchet spaces, Proc. Amer. Math. Soc. 129 (2001), 3759–3760.CrossRefGoogle Scholar
5.Peris, A.Chaotic polynomials on banach spaces, J. Math. Anal. Appl. 287 (2003), 487493.CrossRefGoogle Scholar