Thermal Chaos Of A Charged Dilaton-AdS Black Hole In The Extended Phase Space

Chaos is a kind of very complex motions which appear only in nonlinear and non-integrable dynamic systems.It is not only very sensitive to the initial conditions of the system,but also shows the inherent randomness of the system.General relativity is a kind of highly nonlinear theories in modern physics.Therefore,it is very important to study chaotic behavior in general relativity.In this thesis,the Melnikov method is used to study thermal chaos of dilaton-AdS black hole in the extended phase space.Firstly,we introduce the concept of chaos,the corresponding research methods and the Melnikov method.Make thermal chaos occurred in the Van der Waals fluid and the thermal chaos of the charged AdS black hole as an example of how to apply the Melnikov method.Secondly,we apply the Melnikov method to study the thermal chaos of the charged dilaton-AdS black hole in the extended phase space,and probe the influence of the dilaton parameter on the thermodynamic chaos.For the temporal perturbation,only if the amplitude of the perturbation is larger than a certain critical value,the charged dilaton-AdS black hole appears thermodynamic chaos.For the spatial perturbation,thermal chaos always exists and the occurrence of chaos is independent of the magnitude of the spatial perturbation.These behaviors of thermal chaos in the charged dilaton-AdS black hole are similar to those in other static AdS black holes,which can be regarded as the common features of static AdS black holes.In addition,under the temporal perturbation,the existence of the dilaton parameter make the occurrence of chaos more difficult,which differs from that of the charge parameter.Finally,we present a brief summary and prospect for our work.