First return path derivatives
Author:
Richard J. O’Malley
Journal:
Proc. Amer. Math. Soc. 116 (1992), 73-77
MSC:
Primary 26A24; Secondary 26A21
DOI:
https://doi.org/10.1090/S0002-9939-1992-1097349-4
MathSciNet review:
1097349
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: A new type of path system is introduced. It is motivated by the Poincaré, first return, map of differentiable dynamics. Thus such systems are labeled first return path systems. It is shown that, though these are extremely thin paths, the systems possess interesting intersection properties that make the corresponding differentiation theory as rich as much thicker path systems.
- [1] A. M. Bruckner, R. J. O'Malley, and B. S. Thomson, Path derivatives: A unified view of certain generalized derivatives, Trans. Amer. Math. Soc. 238 (1984), 97-123. MR 735410 (86d:26007)
- [2] A. M. Bruckner, Differentiation of real functions, Lecture Notes in Math., vol. 659, Springer, Berlin and New York, 1978. MR 507448 (80h:26002)
- [3] J. Marcinkiewicz, Sur les nombres dérivés, Fund. Math. 24 (1935), 305-308.
- [4] R. J. O'Malley, Selective derivates, Acta Math. Acad. Sci. Hungar. 29 (1977), 77-97. MR 0437690 (55:10614)
- [5] G. Petruska and M. Laczkovich, Remarks on a problem of A. M. Bruckner, Acta Math. Acad. Sci. Hungar. 38 (1981), 205-214. MR 634581 (83b:26005)
- [6] W. Sierpínski, Sur une propriété de fonctions quelconques d'une variable réele, Fund. Math. 25 (1935), 1-4.
- [7] L. E. Snyder, Continuous Stolz extensions and boundary functions, Trans. Amer. Math. Soc. 119 (1965), 417-427. MR 0180634 (31:4865)
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 26A24, 26A21
Retrieve articles in all journals with MSC: 26A24, 26A21
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1992-1097349-4
Article copyright:
© Copyright 1992
American Mathematical Society