Matching Tag: stokes-phenomena
Fix u 1 , … , u n ∈ \mathds C u_1,\ldots,u_n\in{\mathds C} u 1 , … , u n ∈ \mathds C , ξ ∈ S 1 \xi\in S^1 ξ ∈ S 1 with ℜ ( ( u i − u j ) / ξ ) < 0 \Re((u_i-u_j)/\xi)<0 ℜ (( u i − u j ) / ξ ) < 0 for i < j i<j i < j , and T ∈ M ( n × n , \mathds R ) T\in M(n\times n,{\mathds R}) T ∈ M ( n × n , \mathds R ) upper triangular with T i i = 1 T_{ii}=1 T ii = 1 and T + T t r T+T^{tr} T + T t r positive…
Let ( w , u 1 , … , u n , ξ , T ) (w,u_1,\ldots,u_n,\xi,T) ( w , u 1 , … , u n , ξ , T ) be data with w ∈ \mathds Z w\in{\mathds Z} w ∈ \mathds Z , u i ∈ \mathds C u_i\in{\mathds C} u i ∈ \mathds C pairwise distinct, ξ ∈ S 1 \xi\in S^1 ξ ∈ S 1 satisfying ℜ ( ( u i − u j ) / ξ ) < 0 \Re((u_i-u_j)/\xi)<0 ℜ (( u i − u j ) / ξ ) < 0 for i < j i<j i < j , and…
Let ( H , ∇ , H \mathds R ′ , P ) (H,\nabla,H'_{\mathds R},P) ( H , ∇ , H \mathds R ′ , P ) be a TERP-structure. It requires no ramification when its formal decomposition can be made without ramification; it is a mixed TERP-structure when…
Let ( ν ± , ρ ± ) (\nu^\pm,\rho^\pm) ( ν ± , ρ ± ) be two parameter pairs, and let T ± ( t , ν ± , ρ ± , ℏ ) \mathscr T^\pm(t,\nu^\pm,\rho^\pm,\hbar) T ± ( t , ν ± , ρ ± , ℏ ) be analytic τ \tau τ -functions of ( P I ) (P_{\rm I}) ( P I ) defined on domains containing…
Let ∇ \nabla ∇ be a WKB-regular ℏ \hbar ℏ -flat connection with strongly GMN spectral curve, let Ψ \Psi Ψ be a WKB formal solution, and let \cL Ψ \cL\Psi \cL Ψ be its Borel–Laplace dual. Let…
Let α \alpha α and β \beta β be critical points, let τ ( α ) \tau(\alpha) τ ( α ) and τ ( β ) \tau(\beta) τ ( β ) denote their corresponding torsions, and let S α β \mathcal{S}_{\alpha}^{\beta} S α β be the Stokes coeffici…
Fix ( t , ν ) ∈ D t ∗ × D ν ∗ (t,\nu)\in D_{t_\ast}\times D_{\nu_\ast} ( t , ν ) ∈ D t ∗ × D ν ∗ so that the Stokes graph has no Stokes segment. Let C C C be a Stokes curve connecting a branch point e e e and ∞ \infty ∞ , forming a commo…
Let M > 1 / 2 M>1/2 M > 1/2 , let k k k be any value, and let ψ [ k ] ( 1 ) ( z , z ‾ ; θ ) \psi^{(1)}_{[k]}(z,\overline{z};\theta) ψ [ k ] ( 1 ) ( z , z ; θ ) denote the Symanzik-rescaled solution of the differential equations for ψ ( 1 ) \psi^{(1)} ψ ( 1 ) and…
Let R o d d R_{\rm odd} R odd be the odd part of the formal WKB solution, and let λ ( t , c , η ; α ) \lambda(t,{\bf c},\eta;\alpha) λ ( t , c , η ; α ) be the corresponding transseries solution of ( P I I I ′ ) D 6 (P_{\rm III'})_{D_{6}} ( P II I ′ ) D 6 , with f…