Colloquium

Colloquium
C^1 Approximation of Vector Fields on the Renormalization Group Method 千葉逸人 10月20日(金) 13時30分 The renormalization group (RG) method for differential equations is one of the perturbation methods for obtaining solutions which are approximate to exact solutions uniformly in time. It is shown that for a given vector field on arbitrary manifold, approximate solutions obtained on the RG method define a vector field which is close to an original vector field in $C^1$ topology under appropriate assumptions. Furthermore, some topological properties of the approximate vector field, for instance, the existence of an invariant manifold and its stability, are inherited from the RG equation.

C^1 Approximation of Vector Fields on the Renormalization Group Method

千葉逸人

10月20日(金) 13時30分

The renormalization group (RG) method for differential equations is one of the perturbation methods for obtaining solutions which are approximate to exact solutions uniformly in time. It is shown that for a given vector field on arbitrary manifold, approximate solutions obtained on the RG method define a vector field which is close to an original vector field in $C^1$ topology under appropriate assumptions. Furthermore, some topological properties of the approximate vector field, for instance, the existence of an invariant manifold and its stability, are inherited from the RG equation.