Yulij Ilyashenko

Address: 310 Malott Hall, Ithaca, NY 14853-4201, USA
Gubkina str. 8, Moscow, 119991, Russia

E-mail: yulijs@gmail.com

University: Cornell University
V.A. Steklov Mathematical Institute, RAS

Publications:

Filimonov D. A., Ilyashenko Y. S.

Singular Points in Generic Two-Parameter Families of Vector Fields on a 2-Manifold
2025, vol. 30, no. 2, pp. 279-290

Abstract

In this paper, we give a full description of all possible singular points that occur in generic 2-parameter families of vector fields on compact 2-manifolds. This is a part of a large project aimed at a complete study of global bifurcations in two-parameter families of vector fields on the two-sphere.

Keywords: singularities of vector fields, finite-parameter families of vector fields

Citation: Filimonov D. A., Ilyashenko Y. S., Singular Points in Generic Two-Parameter Families of Vector Fields on a 2-Manifold, Regular and Chaotic Dynamics, 2025, vol. 30, no. 2, pp. 279-290

DOI:10.1134/S1560354725020066

Ilyashenko Y. S.

Thick attractors of step skew products
2010, vol. 15, nos. 2-3, pp. 328-334

Abstract

A diffeomorphism is said to have a thick attractor provided that its Milnor attractor has positive but not full Lebesgue measure. We prove that there exists an open set in the space of boundary preserving step skew products with a fiber [0,1], such that any map in this set has a thick attractor.

Keywords: Milnor attractors, thick attractors, ergodicity

Citation: Ilyashenko Y. S., Thick attractors of step skew products, Regular and Chaotic Dynamics, 2010, vol. 15, nos. 2-3, pp. 328-334

DOI:10.1134/S1560354710020188

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