Skip to Main Content

Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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.

 

Projective sets and ordinary differential equations
HTML articles powered by AMS MathViewer

by Alessandro Andretta and Alberto Marcone PDF
Trans. Amer. Math. Soc. 353 (2001), 41-76 Request permission

Abstract:

We prove that for $n \geq 2$ the set of Cauchy problems of dimension $n$ which have a global solution is $\boldsymbol \Sigma _{1}^{1}$-complete and that the set of ordinary differential equations which have a global solution for every initial condition is $\boldsymbol \Pi _{1}^{1}$-complete. The first result still holds if we restrict ourselves to second order equations (in dimension one). We also prove that for $n \geq 2$ the set of Cauchy problems of dimension $n$ which have a global solution even if we perturb a bit the initial condition is $\boldsymbol \Pi _{2}^{1}$-complete.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 04A15, 34A12
  • Retrieve articles in all journals with MSC (1991): 04A15, 34A12
Additional Information
  • Alessandro Andretta
  • Affiliation: Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy
  • MR Author ID: 314952
  • Email: andretta@dm.unito.it
  • Alberto Marcone
  • Affiliation: Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy
  • Address at time of publication: Dipartimento di Matematica e Informatica, Università di Udine, viale delle Scienze 206, 33100 Udine, Italy
  • Email: marcone@dimi.uniud.it
  • Received by editor(s): March 25, 1998
  • Received by editor(s) in revised form: September 25, 1998
  • Published electronically: April 25, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 41-76
  • MSC (1991): Primary 04A15; Secondary 34A12
  • DOI: https://doi.org/10.1090/S0002-9947-00-02440-5
  • MathSciNet review: 1650065