Archivio della ricerca dell'Università di Modena e Reggio Emiliahttps://iris.unimore.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Tue, 17 May 2022 17:32:44 GMT2022-05-17T17:32:44Z10221Normalization of Poincare' singularities via variation of constantshttp://hdl.handle.net/11380/310260Titolo: Normalization of Poincare' singularities via variation of constants
Abstract: We present a geometric proof of the Poincare-Dulac Normalization Theorem for analytic vector fields with singularities of Poincare type. Our approach allows us to relate the size of the convergence domain of the linearizing transformation to the geometry of the complex foliation associated to the vector field. A similar construction is considered in the case of linearization of maps in a neighborhood of a hyperbolic fixed point.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/11380/3102602005-01-01T00:00:00ZAlgebraic nonsolvability of the problem of existence of holomorphic first integralshttp://hdl.handle.net/11380/460004Titolo: Algebraic nonsolvability of the problem of existence of holomorphic first integrals
Abstract: We prove that the problem of existence of holomorphic first integrals of analytic differential equations in a neighbourhood of a singular point is not algebraically solvable
Sun, 01 Jan 1995 00:00:00 GMThttp://hdl.handle.net/11380/4600041995-01-01T00:00:00ZSome properties of planar polynomial systems of even degreehttp://hdl.handle.net/11380/585937Titolo: Some properties of planar polynomial systems of even degree
Abstract: We prove that a planar polynomial vector field of even degree always has an unbounded solution
Wed, 01 Jan 1992 00:00:00 GMThttp://hdl.handle.net/11380/5859371992-01-01T00:00:00ZLimit cycles and bifurcation from a separatrix for a polynomial Lienard system in the plane.http://hdl.handle.net/11380/640398Titolo: Limit cycles and bifurcation from a separatrix for a polynomial Lienard system in the plane.
Abstract: We study bifurcations of limit cycles from a separatrix in a polynomial Lienard equation.
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/11380/6403981997-01-01T00:00:00ZError bounds for solutions of systems of quasilinear hyperbolic partial differential equations in bicharacteristic formhttp://hdl.handle.net/11380/640379Titolo: Error bounds for solutions of systems of quasilinear hyperbolic partial differential equations in bicharacteristic form
Abstract: We find bounds for the difference between the solutions of a nonlinear systems of hyperbolic differential equations in bicharacteristic form and its linear counterpart.
Wed, 01 Jan 1986 00:00:00 GMThttp://hdl.handle.net/11380/6403791986-01-01T00:00:00ZGeometric bounds on the linearization domain and analytic dependence on parameters for families of analytic vector fields in a neighborhood ofa singular pointhttp://hdl.handle.net/11380/715637Titolo: Geometric bounds on the linearization domain and analytic dependence on parameters for families of analytic vector fields in a neighborhood ofa singular point
Abstract: We study families of holomorphic vector fields, holomorphically depending on parameters,in a neighborhood of an isolated singular point. When the singular point is in the Poincarédomain for every vector field of the family we prove, through a modification of classicalSternberg’s linearization argument, cf. Nelson (1969) [7] too, analytic dependence onparameters of the linearizing maps and geometric bounds on the linearization domain:each vector field of the family is linearizable inside the smallest Euclidean sphere which isnot transverse to the vector field, cf. Brushlinskaya (1971) [2], Ilyashenko and Yakovenko(2008) [5] for related results. We also prove, developing ideas in Martinet (1980) [6],a version of Brjuno’s Theorem in the case of linearization of families of vector fields neara singular point of Siegel type, and apply it to study some 1-parameter families of vectorfields in two dimensions.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/11380/7156372011-01-01T00:00:00ZJets of differential equations having integrable extensionshttp://hdl.handle.net/11380/460006Titolo: Jets of differential equations having integrable extensions
Abstract: We characterize the set of $n$-jets admitting an extension which is a germ of a differential equation with an analytic first integral, and compute its codimension in the $n$-jet space. Some applications in the case of the centre-focus problem are given.
Thu, 01 Jan 1998 00:00:00 GMThttp://hdl.handle.net/11380/4600061998-01-01T00:00:00ZOn the Poincare'-Lyapunov Centre theoremhttp://hdl.handle.net/11380/460007Titolo: On the Poincare'-Lyapunov Centre theorem
Abstract: We give a geometric proof and a slight generalization of a result of Sibuya and Urabe concerning a higher dimensional version of the classical Poincaré-Lyapunov Centre Theorem. This is done from a complexified point of view.
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/11380/4600071999-01-01T00:00:00ZOn the problem of existence of holomorphic first integralshttp://hdl.handle.net/11380/460003Titolo: On the problem of existence of holomorphic first integrals
Abstract: We discuss the Mattei-Moussu topological criterion for existence of a holomorphic first integral in a neighbourhood of a singular point of an analytic differential equation, and we prove that it cannot be used to get algebraic solvability of such an existence problem.
Sun, 01 Jan 1995 00:00:00 GMThttp://hdl.handle.net/11380/4600031995-01-01T00:00:00ZPeriodic orbits for vector fields with nondegenerate first integralshttp://hdl.handle.net/11380/309768Titolo: Periodic orbits for vector fields with nondegenerate first integrals
Abstract: We give a geometric proof in the particular case of nondegenerate first integrals. of a theorem by Moser about the existence of periodic orbits on each level set of the integral, in a neighbourhood of a singular point of a vector field satisfying a nonresonance hypothesis. We use the same geometric approach to deal with the resonance case, obtaining a generalization of previous results by Sweet.
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/11380/3097682001-01-01T00:00:00Z