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- J. Yang, I. Kupka, Z. Schuss, D. Holcman
- Journal of mathematical biology
- 2016

The search by swimmers for a small target in a bounded domain is ubiquitous in cellular biology, where a prominent case is that of the search by spermatozoa for an egg in the uterus. This is one of the severest selection processes in animal reproduction. We present here a mathematical model of the search, its analysis, and numerical simulations. In the… (More)

- David Holcman, Ivan Kupka
- 2004

On a compact Riemannian manifold (V m , g), we consider the second order positive operator L ǫ = ǫ∆ g + (b, ∇) + c, where −∆ g is the Laplace-Beltrami operator and b is a Morse-Smale (MS) field, ǫ a small parameter. We study the measures which are the limits of the normalized first eigenfunctions of L ǫ as ǫ goes to the zero. In the case of a general MS… (More)

In this Note we present some results concerning the concentration of sequences of first eigenfunctions on the limit sets of a Morse–Smale dynamical system on a compact Riemannian manifold. More precisely a renormalized sequence of eigenfunctions converges to a measure µ concentrated on the hyperbolic sets of the field. The coefficients which appear in the… (More)

- David Holcman, Ivan Kupka
- 2005

We study the semi-classical limits of the first eigenfunction of a positive second order operator on a compact Riemannian manifold when the diffusion constant ǫ goes to zero. We assume that the first order term is given by a vector field b, whose recurrent components are either hyperbolic points or cycles or two dimensional torii. The limits of the… (More)

- Assaf Amitai, Ivan Kupka, David Holcman
- Multiscale Modeling & Simulation
- 2012

- Jacques Féjoz, A. Neishtadt, +26 authors Richard Mont
- 2012

- David Holcman, Ivan Kupka
- 2008

We study the semi-classical limits of the first eigenfunction of a positive second order operator on a compact Riemannian manifold, when the diffusion constant ǫ goes to zero. If the drift of the diffusion is given by a Morse-Smale vector field b, the limits of the eigenfunctions concentrate on the recurrent set of b. A blow-up analysis enables us to find… (More)

- David Holcman, Ivan Kupka
- 2002

In this paper, we give explicit estimates that insure the existence of solutions for first order partial differential operators on compact manifolds, using a viscosity method. In the linear case, an explicit integral formula can be found, using the characteristics curves. The solution is given explicitly on the critical points and the limit cycles of the… (More)

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