Opuscula Math. 36, no. 4 (2016), 471-479

Opuscula Mathematica

A remark on the intersections of subanalytic leaves

Maciej P. Denkowski

Abstract. 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.

Keywords: transversality conditions, subanalytic sets.

Mathematics Subject Classification: 32B20, 70H33.

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  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 à 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, Densité 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), 368-384.
  • Maciej P. Denkowski
  • Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Mathematics, Łojasiewicza 6, 30-348 Kraków, Poland
  • Communicated by Yoshishige Haraoka.
  • Received: 2015-09-09.
  • Revised: 2016-01-25.
  • Accepted: 2016-02-05.
  • Published online: 2016-04-01.
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Cite this article as:
Maciej P. Denkowski, A remark on the intersections of subanalytic leaves, Opuscula Math. 36, no. 4 (2016), 471-479, http://dx.doi.org/10.7494/OpMath.2016.36.4.471

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