00778nas a2200133 4500008004100000245004800041210004700089260001000136520038900146653002700535100002500562700002100587856003600608 2010 en d00aDynamics control by a time-varying feedback0 aDynamics control by a timevarying feedback bSISSA3 aWe consider a smooth bracket generating control-affine system in R^d and show that any orientation preserving diffeomorphism of R^d can be approximated, in the very strong sense, by a diffeomorphism included in the flow generated by a time-varying feedback control which is polynomial with respect to the state variables and trigonometric-polynomial with respect to the time variable.10aDiscrete-time dynamics1 aAgrachev, Andrei, A.1 aCaponigro, Marco uhttp://hdl.handle.net/1963/646100583nas a2200109 4500008004300000245005200043210005200095520024400147100002500391700002100416856003600437 2009 en_Ud 00aControllability on the group of diffeomorphisms0 aControllability on the group of diffeomorphisms3 aGiven a compact manifold M, we prove that any bracket generating family of vector fields on M, which is invariant under multiplication by smooth functions, generates the connected component of identity of the group of diffeomorphisms of M.1 aAgrachev, Andrei, A.1 aCaponigro, Marco uhttp://hdl.handle.net/1963/3396