Estimation Of Topological Entropy Of Nonautonomous Dynamical Systems And Non - Compact Nonautonomous Inverse Topological Pressure

Topological entropy is nonnegative real numbers or infinity, which corre-sponds to the continous map in compact topological space. So far it is the only topological conjugate numerical invariant, so there are many experts in the field of mathematics and theoretical physics paying attention to it over the years. The estimation and calculation of topological entropy become an impor-tant subjet in the field of dynamical system. First, we define exponential ex-tension in autonomous dynamical system, and the exponential extension prove exponential convergence of topological entropy, so the exponential extension is the sufficient condition of the E.Ghys conjecture equation.Second, we define topological sup-entropy, topological inf-entropy in Non-autonomous dynamical system, and estimate topological entropy, topological sup-entropy, topological inf-entropy. Topological pressure is the generalization of topological entropy and it is widely used in thermodynamic theory and dimension theory. Third,we define topological pressure, upper Caratheodory-pesin and lower Caratheodory-pesin in noncompact non-autonomous proper dynamical system and study the related properties.