01295nas a2200133   4500008004100000245006800041210006800109300001200177490000700189520087800196100002001074700002101094856004601115       2017                        eng d00aAnalytic geometry of semisimple coalescent Frobenius structures0 aAnalytic geometry of semisimple coalescent Frobenius structures  a17400040 v063 a<p>We present some results of a joint paper with Dubrovin (see references), as exposed at the Workshop “Asymptotic and Computational Aspects of Complex Differential Equations” at the CRM in Pisa, in February 2017. The analytical description of semisimple Frobenius manifolds is extended at semisimple coalescence points, namely points with some coalescing canonical coordinates although the corresponding Frobenius algebra is semisimple. After summarizing and revisiting the theory of the monodromy local invariants of semisimple Frobenius manifolds, as introduced by Dubrovin, it is shown how the definition of monodromy data can be extended also at semisimple coalescence points. Furthermore, a local Isomonodromy theorem at semisimple coalescence points is presented. Some examples of computation are taken from the quantum cohomologies of complex Grassmannians.</p>1 aCotti, Giordano1 aGuzzetti, Davide  uhttps://doi.org/10.1142/S201032631740004400665nas a2200109   4500008004100000245007400041210007100115260001900186520029300205100002100498856003600519       2011                        en  d00aAn asymptotic reduction of a Painlevé VI equation to a Painlevé III0 aasymptotic reduction of a Painlevé VI equation to a Painlevé III  bIOP Publishing3 aWhen the independent variable is close to a critical point, it is shown that\\r\\nPVI can be asymptotically reduced to PIII. In this way, it is possible to\\r\\ncompute the leading term of the critical behaviors of PVI transcendents\\r\\nstarting from the behaviors of PIII transcendents.1 aGuzzetti, Davide  uhttp://hdl.handle.net/1963/512400921nas a2200121   4500008004100000245012500041210006900166260004700235520035300282100002100635700002100656856012200677       2007                        en  d00aThe Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials II: L.I.F.S. Measures and Quantum Mechanics0 aAsymptotic Behaviour of the Fourier Transforms of Orthogonal Pol  b2007 Birkh¨auser Verlag Basel/Switzerland3 aWe study measures generated by systems of linear iterated functions,\r\ntheir Fourier transforms, and those of their orthogonal polynomials. We\r\ncharacterize the asymptotic behaviours of their discrete and continuous averages.\r\nFurther related quantities are analyzed, and relevance of this analysis\r\nto quantum mechanics is briefly discussed1 aGuzzetti, Davide1 aMantica, Giorgio  uhttps://math.sissa.it/publication/asymptotic-behaviour-fourier-transforms-orthogonal-polynomials-ii-lifs-measures-and