Asymptotic behavior of solutions of systems of dynamic equations on time scales in a set whose boundary is a combination of strict egress and strict ingress points

In this paper we study the asymptotic behavior of solutions of nonlinear dynamic systems on time scales of the formyΔ(t)=f(t,y(t)),yΔ(t)=f(t,y(t)),where f:T×Rn→Rnf:T×Rn→Rn and TT is a time scale. For a given set Ω⊂T×RnΩ⊂T×Rn, we formulate the conditions for function f, which guarantee that at least one solution y   of the above system stays in ΩΩ. The dimension of the space of initial data generating such solutions is discussed and perturbed linear systems are considered as well. A linear system with singularity at infinity is considered as an example.