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D. Vokrouhlick\'y, M. Bro\v z (Univ. Prague), P. Farinella (Univ. Trieste), Z. Kne\v zevi\`c (Belgrade Obs.)
The non--gravitational Yarkovsky effect can shift the semimajor axis of small asteroids up to \approx 20~km in size by \approx 0.01~AU. This mobility increases the supply of multi--km bodies to the near--Earth asteroid population, but may have other consequences related to the dynamics of main--belt asteroids, in particular those which are near the edges of the Kirkwood gaps. We have integrated the orbits of asteroids 2953 Vysheslavia, 1991 UA2, 1993 FR58 (plus a number of ``dynamical clones'' of these bodies) which all lie very close to the outer border of the powerful 5:2 resonance. Our simulations typically span 250~Myr and take into account gravitational perturbations due to the outer planets (except Pluto) and both components (diurnal and seasonal) of the Yarkovsky effect. Vysheslavia is a member of the Koronis family, but is presently locked in a region that exhibits chaotic dynamics, a coincidence which motivated some earlier studies on its origin and evolution. Although our simulations do not reproduce the very short lifetime of Vysheslavia reported in earlier studies (possibly due to the use of a different integrator), we confirm the complex dynamical structure of the region just outside the 5:2 resonance. In particular, Vysheslavia is trapped in a layer characterized by ``stable chaos'', and typically it stays there for at least 100~Myr. Other small members of the Koronis family, which were originally located very close to this region, may reach it by Yarkovsky drift in 50--500~Myr (depending on their size, thermal parameters and the orientation of their spin axis). A temporary capture spanning tens to hundreds Myr in the thin chaotic layer is then possible, until eventually the body falls into the 5:2 resonance. Such an evolutionary scenario might apply both to Vysheslavia itself (in the past) and to other nearby members of the Koronis family (in the future).