论文标题
对一个自一致转移操作员家族的线性响应
Linear Response for a Family of Self-Consistent Transfer Operators
论文作者
论文摘要
我们研究了在热力学极限下全部弱耦合均匀扩展的圆图的系统。系统的状态通过概率度量来描述，其演变由非线性操作员的作用给出，也称为自洽传输操作员。我们证明，当耦合足够小时，系统具有独特的稳定状态，在改变耦合强度时可以满足线性响应公式。
We study a system of all-to-all weakly coupled uniformly expanding circle maps in the thermodynamic limit. The state of the system is described by a probability measure and its evolution is given by the action of a nonlinear operator, also called a self-consistent transfer operator. We prove that when the coupling is sufficiently small, the system has a unique stable state that satisfies a linear response formula when varying the coupling strength.
