Basic Global Relative Invariants for Homogeneous Linear Differential Equations

Released on by Roger Chalkley
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  • Basic Global Relative Invariants for Homogeneous Linear Differential Equations Book Detail

  • Author : Roger Chalkley
  • Release Date : 2002
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 223
  • ISBN 13 : 0821827812
  • File Size : 60,60 MB
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Basic Global Relative Invariants for Homogeneous Linear Differential Equations by Roger Chalkley PDF Summary

Book Description: Given any fixed integer $m \ge 3$, the author presents simple formulas for $m - 2$ algebraically independent polynomials over $\mathbb{Q}$ having the remarkable property, with respect to transformations of homogeneous linear differential equations of order $m$, that each polynomial is both a semi-invariant of the first kind (with respect to changes of the dependent variable) and a semi-invariant of the second kind (with respect to changes of the independent variable). These relative invariants are suitable for global studies in several different contexts and do not require Laguerre-Forsyth reductions for their evaluation. In contrast, all of the general formulas for basic relative invariants that have been proposed by other researchers during the last 113 years are merely local ones that are either much too complicated or require a Laguerre-Forsyth reduction for each evaluation.

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