A remark on the intersections of subanalytic leaves

• Autorzy: Denkowski M. P.

Identyfikatory

DOI

10.7494/OpMath.2016.36.4.471

• Języki publikacji: EN

Abstrakty

EN

We discuss a new sufficient condition - weaker than the usual transversality condition - for the intersection of two subanalytic leaves to be smooth. It involves the tangent cone of the intersection and, as typically non-transversal, it is of interest in analytic geometry or dynamical systems. We also prove an identity principle for real analytic manifolds and subanalytic functions.

Słowa kluczowe

EN

transversality conditions; subanalytic sets

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2016
• Tom: Vol. 36, no. 4
• Strony: 471--479
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Denkowski M. P.

• Jagiellonian University Faculty of Mathematics and Computer Science Institute of Mathematics Łojasiewicza 6, 30-348 Kraków, Poland

Bibliografia

• [1] L. Birbrair, M.P. Denkowski, Medial axis and singularities (2015), submitted.
• [2] Z. Denkowska, M.P. Denkowski, The Kuratowski convergence and connected components, J. Math. Anal. Appl. 387 (2012) 1, 48-65.
• [3] Z. Denkowska, J. Stasica, Ensembles sous-analytiques a la polonaise, Hermann Paris, 2007.
• [4] M.P. Denkowski, R. Pierzchała, On the Kuratowski convergence of analytic sets, Ann. Polon. Math. 93 (2008) 2, 101-112.
• [5] K. Kurdyka, G. Raby, Densite des ensembles sous-analytiques, Ann. Inst. Fourier 39 (1985) 3, 753-771.
• [6] J. Palis, Moduli of stability and bifurcation theory, Proc. Int. Cong, of Mathematicians, Helsinki (1978), 835-839.
• [7] J. Palis, W. de Melo, Moduli of stability of diffeomorphisms, Springer Lect. Notes in Math. 819 (1980), 315-339.
• [8] F. Takens, Moduli and bifurcations: non-transversal intersections of invariant manifolds and vector fields, [in:] Functional Differential Equations and Bifurcations, Lecture Notes in Math. 799 (1980), 368-38

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.