# Generic one-parameter families of vector fields on two-dimensional manifolds

@article{Sotomayor1974GenericOF, title={Generic one-parameter families of vector fields on two-dimensional manifolds}, author={Jorge Sotomayor}, journal={Publications Math{\'e}matiques de l'Institut des Hautes {\'E}tudes Scientifiques}, year={1974}, volume={43}, pages={5-46} }

## 83 Citations

Generic bifurcation of reversible vector fields on a 2-dimensional manifold

- Mathematics
- 1997

In this paper we deal with reversible vector fields on a 2-dimensional manifold having a codimension one submanifold as its symmetry axis. We classify generically the one parameter families of such…

Bifurcations at a cusp singularity with applications

- Mathematics
- 1984

We consider families of vector fields which exhibit a cusp singularity for some values of the parameters. Algebraic conditions are obtained for these families to have versal properties. This enables…

Bifurcations of Umbilic Points and Related Principal Cycles

- Mathematics
- 2004

The simplest patterns of qualitative changes on the configurations of lines of principal curvature around umbilic points on surfaces whose immersions into ℝ3 depend smoothly on a real parameter…

Homotopically unbounded disks for generic surface diffeomorphisms

- Mathematics
- 2022

In this paper we consider closed orientable surfaces S of positive genus and Cr-diffeomorphisms f : S → S isotopic to the identity (r ≥ 1). The main objective is to study periodic open topological…

Numeric invariants in semilocal bifurcations

- Mathematics
- 2020

Bifurcations that occur in a small neighborhood of a polycycle of a planar vector field are called semilocal. We prove that even semilocal bifurcations of hyperbolic polycycles may have numeric…

Plenty of unbounded periodic disks for families of surface diffeomorphisms

- Mathematics
- 2020

In this paper we consider closed orientable surfacesM of positive genus and diffeomorphisms f : M →M. The main objective is to show that such maps, under certain natural conditions and some generic…

Global Bifurcations in Generic One-Parameter Families with a Parabolic Cycle on S 2

- MathematicsMoscow Mathematical Journal
- 2019

We classify global bifurcations in generic one-parameter local families of \vfs on $S^2$ with a parabolic cycle. The classification is quite different from the classical results presented in…

New structurally unstable families of planar vector fields

- Mathematics
- 2019

We study global bifurcations in generic three-parameter families of vector fields on S 2. In the recent article by Ilyashenko et al (2018 Invent. Math. 213 461--506), the authors show that…

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