First return path derivatives
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- by Richard J. O’Malley PDF
- Proc. Amer. Math. Soc. 116 (1992), 73-77 Request permission
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.References
- A. M. Bruckner, R. J. O’Malley, and B. S. Thomson, Path derivatives: a unified view of certain generalized derivatives, Trans. Amer. Math. Soc. 283 (1984), no. 1, 97–125. MR 735410, DOI 10.1090/S0002-9947-1984-0735410-1
- Andrew M. Bruckner, Differentiation of real functions, Lecture Notes in Mathematics, vol. 659, Springer, Berlin, 1978. MR 507448, DOI 10.1007/BFb0069821 J. Marcinkiewicz, Sur les nombres dérivés, Fund. Math. 24 (1935), 305-308.
- R. J. O’Malley, Selective derivates, Acta Math. Acad. Sci. Hungar. 29 (1977), no. 1-2, 77–97. MR 437690, DOI 10.1007/BF01896470
- M. Laczkovich and G. Petruska, Remarks on a problem of A. M. Bruckner, Acta Math. Acad. Sci. Hungar. 38 (1981), no. 1-4, 205–214. MR 634581, DOI 10.1007/BF01917534 W. Sierpínski, Sur une propriété de fonctions quelconques d’une variable réele, Fund. Math. 25 (1935), 1-4.
- Larry E. Snyder, Continuous Stolz extensions and boundary functions, Trans. Amer. Math. Soc. 119 (1965), 417–427. MR 180634, DOI 10.1090/S0002-9947-1965-0180634-6
Additional Information
- © Copyright 1992 American Mathematical Society
- 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