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  • 1
    Electronic Resource
    Electronic Resource
    Local extrema of analytic functions (1996)
    Springer
    Nonlinear differential equations and applications 3 (1996), S. 287-303 
    Details
    ISSN: 1420-9004
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give a complete answer to the problem of the finite decidability of the local extremality character of a real analytic function at a given point, a problem that found partial answers in some works by Severi and Łojasiewicz. Consider a real analytic functionf defined in a neighbourhood of a pointx 0∈R n . Restrictf to the spherical surface centered inx 0 and with radiusr≥0 and take its infimumm(r) and its supremumM(r). We establish some properties ofm(r) andM(r) for smallr〉0. In particular, we prove that they have asymptotic expansions of the formf(x 0)+c·(r α+o(r α)) asr→0 for a realc and a rational α≥1 (of course the parameters will usually be different form andM).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01194068
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Stability of some Central Forces (1999)
    Springer
    Nonlinear differential equations and applications 6 (1999), S. 289-296 
    Details
    ISSN: 1420-9004
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. In this paper we deal with attractive central forces, more precisely with the system¶¶ $\ddot{x} = -xf(x,y), \,\, {\ddot{y}} = -yf(x,y), \,\, f(0,0) \ge 0.$ ¶¶We characterize the stability of the origin whenever the system admits a first integral of the following kind¶¶ $V(x,y,{\dot{x}},{\dot{y}}) = a{\dot{x}}^2 + b{\dot{x}}{\dot{y}} + c{\dot{y}}^2 + {\rm{II}}(x,y).$
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s000300050077
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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