scholarly journals Quasianalytic Ilyashenko Algebras

2018 ◽  
Vol 70 (1) ◽  
pp. 218-240 ◽  
Author(s):  
Patrick Speissegger

AbstractWe construct a quasianalytic field of germs at +∞ of real functions with logarithmic generalized power series as asymptotic expansions, such that is closed under differentiation and log-composition; in particular, is a Hardy field. Moreover, the field o (−log) of germs at 0+ contains all transition maps of hyperbolic saddles of planar real analytic vector fields.

2010 ◽  
Vol 59 (1-2) ◽  
pp. 125-139
Author(s):  
Víctor Castellanos ◽  
Abel Castorena ◽  
Manuel Cruz-López

Author(s):  
Shou-Fu Tian ◽  
Mei-Juan Xu ◽  
Tian-Tian Zhang

Under investigation in this work is a generalized higher-order beam equation, which is an important physical model and describes the vibrations of a rod. By considering Lie symmetry analysis, and using the power series method, we derive the geometric vector fields, symmetry reductions, group invariant solutions and power series solutions of the equation, respectively. The convergence analysis of the power series solutions are also provided with detailed proof. Furthermore, by virtue of the multipliers, the local conservation laws of the equation are derived as well. Furthermore, an effective and direct approach is proposed to study the symmetry-preserving discretization for the equation via its potential system. Finally, the invariant difference models of the generalized beam equation are successfully constructed. Our results show that it is very useful to construct the difference models of the potential system instead of the original equation.


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