An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension
V. Kaloshin, M. Saprykina, Communications in Mathematical Physics 315 (2012) 643–697.

Generic diffeomorphisms with superexponential growth of number of periodic orbits
V. Kaloshin, Communications in Mathematical Physics 211 (2000) 253–271.

How projections affect the dimension spectrum of fractal measures
B.R. Hunt, V. Kaloshin, Nonlinearity 10 (1997) 1031–1046.