Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Chaotic polynomials on Fréchet spaces
HTML articles powered by AMS MathViewer

by Alfredo Peris PDF
Proc. Amer. Math. Soc. 127 (1999), 3601-3603 Request permission

Abstract:

Contrary to the case of polynomials on Banach spaces, in which it is known that no hypercyclic homogeneous polynomial of degree $m \geq 2$ exists on any Banach space, we construct for each $m \geq 2$ a chaotic $m$-homogeneous polynomial $P$ on the Fréchet space $\mathcal {H}(\mathbb {C} )$.
References
  • J. Banks, J. Brooks, G. Cairns, G. Davis, and P. Stacey, On Devaney’s definition of chaos, Amer. Math. Monthly 99 (1992), no. 4, 332–334. MR 1157223, DOI 10.2307/2324899
  • N. C. Bernardes, On orbits of polynomial maps in Banach spaces, Quaestiones Math. (to appear).
  • Robert L. Devaney, An introduction to chaotic dynamical systems, 2nd ed., Addison-Wesley Studies in Nonlinearity, Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1989. MR 1046376
  • Seán Dineen, Complex analysis in locally convex spaces, Notas de Matemática [Mathematical Notes], vol. 83, North-Holland Publishing Co., Amsterdam-New York, 1981. MR 640093
  • P. Hebroni, Sur les inverses des éléments dérivables dans un anneau abstrait, C. R. Acad. Sci. Paris 209 (1939), 285–287 (French). MR 14
  • R. Meise, D. Vogt, Introduction to Functional Analysis, Oxford Univ. Press, 1997.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46G20, 46A04, 58F08
  • Retrieve articles in all journals with MSC (1991): 46G20, 46A04, 58F08
Additional Information
  • Alfredo Peris
  • Affiliation: Departamento de Matemática Aplicada, E.T.S. Arquitectura, Universidad Politécnica de Valencia, E-46071 Valencia, Spain
  • Email: aperis@pleiades.upv.es
  • Received by editor(s): December 29, 1997
  • Received by editor(s) in revised form: February 17, 1998
  • Published electronically: May 13, 1999
  • Additional Notes: This research was supported in part by DGICYT under Proyecto PB94-0541.
  • Communicated by: Theodore W. Gamelin
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 3601-3603
  • MSC (1991): Primary 46G20, 46A04, 58F08
  • DOI: https://doi.org/10.1090/S0002-9939-99-04937-0
  • MathSciNet review: 1610769