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Vladimir Lazutkin

St.-Petersburg, Ulyanovskaya str., 1/1, Petrodvorec
St.-Petersburg State University


Igotti N. N., Lazutkin V. F.
Existence of complex homoclinic points
2000, vol. 5, no. 4, pp.  383-400
A method of proving the existence of a local transversal intersection between two immersed holomorphic curves in $\mathbb{C}^2$ is suggested. It is based on an application of the inverse function theorem, the corresponding inequalities being checked numerically. The method is applied to the problem of interpretation of tips of ferns on the unstable manifold of the semistandard map as complex homoclinic points.
Citation: Igotti N. N., Lazutkin V. F.,  Existence of complex homoclinic points, Regular and Chaotic Dynamics, 2000, vol. 5, no. 4, pp. 383-400
Lazutkin V. F.
Making Fractals Fat
1999, vol. 4, no. 1, pp.  51-69
An explicit contruction of a nonuniformly hyperbolic invariant set of positive Lebesgue measure in the phase space of an area-preserving map is suggested. The construction is based on the study of the web created by the stable and unstable manifolds of fixed hyperbolic points.
Citation: Lazutkin V. F.,  Making Fractals Fat, Regular and Chaotic Dynamics, 1999, vol. 4, no. 1, pp. 51-69
Giorgilli A., Lazutkin V. F., Simo C.
Visualization of a Hyperbolic Structure in Area Preserving Maps
1997, vol. 2, nos. 3-4, pp.  47-61
We present a simple method which displays a hyperbolic structure in the phase space of an area preserving map. The method is illustrated for the case of the Carleson standard map. As it follows from our experiments, the structure of the chaotic zone for the standard map is different from the one found for the systems of Anosov type.
Citation: Giorgilli A., Lazutkin V. F., Simo C.,  Visualization of a Hyperbolic Structure in Area Preserving Maps, Regular and Chaotic Dynamics, 1997, vol. 2, nos. 3-4, pp. 47-61
Lazutkin V. F.
Interfering Combs and a Multiple Horseshoe
1997, vol. 2, no. 2, pp.  3-13
If two identical combs overlap with a small shift, this displays an interfering picture. We analyze this phenomenon and consider an application to creating a hyperbolic invariant set in the phase space of an area preserving map.
Citation: Lazutkin V. F.,  Interfering Combs and a Multiple Horseshoe, Regular and Chaotic Dynamics, 1997, vol. 2, no. 2, pp. 3-13

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