Opuscula Math. 36, no. 4 (2016), 471-479
http://dx.doi.org/10.7494/OpMath.2016.36.4.471

 
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.

Full text (pdf)

  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.
Opuscula Mathematica - cover

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

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.