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The pathology of differential equations

Published online by Cambridge University Press:  09 April 2009

T. M. Cherry
T. M. Cherry
Affiliation:
University of Melbourne
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Abstract

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Type
Presidental Address
Information
Journal of the Australian Mathematical Society , Volume 1 , Issue 1 , August 1959 , pp. 1 - 16
Copyright
Copyright © Australian Mathematical Society 1959

References

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Hadamard, J., J. de Math. [5] 4 (1898), 29. Considering a surface of negative curvature of genus exceeding 1, he shows that the set of those geodesics which do not run off ultimately to infinity is a pathological component of the set of all geodesics.Google Scholar
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[6]Cherry, T. M., Proc. Cambridge Phil. Soc. 22 (1924), 325. The result was known in 1920 by Birkhoff and guessed, but not proved, by Whittaker E. T., Proc. Roy. Soc. Edinburgh 37 (1916), 95. Apparently, and surprisingly, it seems to have remained unnoticed by Poincaré.CrossRefGoogle Scholar
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[16]See for example Fatou, P., Bull. Soc. Math. France 47 (1919), 161 at Sec. 8.CrossRefGoogle Scholar
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