Codimension-two Singularities Of Reversible Vector Fields In 3d

This paper is concerned with the dynamics near an equilibrium point of reversible systems. For a large class of reversible vector fields on the three dimensional space we present all the topological types and their respective normal forms of the codimension-two symmetric singularities. Such classification comes from useful new results, also proved here, on dynamical systems defined on manifolds with boundary.22399428Arnold, V.I., Indices of Singular Points of 1-forms on a Manifold with Boundary (1979) Russian Math. Surveys, 34 (2), pp. 1-42. , Convolution of Invariants of Reflection Groups, and Singular Projection of Smooth SurfacesArnold, V.I., Normal Forms for Functions near Degenerate Critical Points (1972) The Weil Groups of Ak, Dk, Ek, and Lagrangian Singularities, 6, pp. 254-272Arnold, V.I., On Local Problems of Analysis (1970) Vestn. Mos. UN-TA, Matematika, Mekhan, 25 (2), pp. 52-56Lamb, J.S.W., (1994) Reversing Symmetries In Dynamical Systems, , Thesis, University of AmsterdamMedrado, J.C.R., Teixeira, M.A., (1998) Symmetric Singularities of Reversible Vector Fields In Dimension Three, 112, pp. 122-131. , "Physica D"Melo, W., Palis, J., (1982) Geometric Theory of Dynamical Systems, , an introduction, Springer Verlag, NYRieger, J.H., Versal Topological Stratification and the bifurcation geometry of Map Germs of the Plane (1990) Math. Proc. Camb. Phil. Soc, 107, pp. 127-147Sevryuk, M.B., (1986) Reversible Systems, p. 1211. , Edited by A.Dold and B. Eckmann, Springer-VerlagSotomayor, J., Generic One-Parameter of vector Fields on Two-Dimensional Manifolds (1974), 43, pp. 5-46Sotomayor, J., Teixeira, M.A., Vector fields near the boundary of for 3-manifold (1988) Lecture Notes In Mathematics, 1331, pp. 169-195. , Springer-VerlagTeixeira, M.A., (1996) Singularities of Reversible Vector Fields, 1482, pp. 1-18. , "Physica D"Teixeira, M.A., (2000) Local Reversibility and Applications, pp. 251-265. , "Real and Complex Singularities, Ed. Bruce J. W. and Tari, F.",412, Research Notes in Mathmatics, Chapman&Hall/CRCVishik, S.M., Vector Fields near the Boundary of the Manifold (1972) Vestnik Moskovskogo Universiteta Matematika, 27, pp. 21-28Yang, J., Polynomial normal forms for vector fields on IR 3, Duke (2001) Math. J, 106, pp. 1-1