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 books.google.com D.V. Anosov, V.I. Arnold  1997  Preview If A, A2<0, then the singular point of the equation x — Ax is a saddle point (Fig. 2
a); if At and A2 are real and have the ... the Euclidean volume of the image. Basic
Concepts 21 Saddles, Nodes, Foci, Centers The LiouvilleOstrogradsky Formula. 

 books.google.com Equations. Consider the homogeneous linear secondorder DE with variable
coefficients p0(x)y + p1(x)y + p2(x)y =0, (6.1) ... For the Wronskian defined in (6.2)
the following Abel's identity (also known as the Ostrogradsky–Liouville formula) ... 

 books.google.com Assume that for some X £ C the equation (6.78) has a nontrivial almost periodic
solution x(t). ... The formulas that we construct are generalizations of the well
known D'AlembertLiouvilleOstrogradsky formula y{t) = u{t) I u2{£,)dZ (6.81) . 

 books.google.com This is however an immediate consequence of the LiouvilleOstrogradsky
formula (5.3). It is clear that rank ^4.6 < rank A for arbitrary matrices. From (5.28)
we therefore get rank Fn,fc < rank (adj Pn)(lk~^(xn,k) = Ik On the other hand from
(5.4) ... 

 books.google.com By using the three term recurrence formula it is straightforward to prove some
algebraic formulas which are important in the theory, such as nl P^^AMw)  P*n{z
)A*nP^1{w) = (w ... the LiouvilleOstrogradsky formula: Qn(z)PZi(z)Pn(z)<? 

 books.google.com ... (11.43) By substituting w(g) = yw(jc) into (11.43) a hypergeometric differential
equation is obtained with parameters a,b,c. ... by means of the Liouville
Ostrogradsky formula we find c2(l+g2)^ = Q2ax + X □ where c2 = lime^o g2ax +
l j '(£?) ... 

 books.google.com Expanding the determinant according to the elements of the last column, we get
from (11.6) an equation of the form ... Liouville's* formula: W(x) = W(x0)e *° *
Ostrogradsky, M. V. (18011861), a Russian mathematician; Liouville, Joseph ... 

 books.google.com ... H HeineBorel lemma Hyperplane 6 171 Inhomogeneous equation 50 —
system 3, 14, 22, 34, 49, 55 Invariant manifold ... Osgood theorem 138
OstrogradskyLiouville relation 98 Perron theorem 72 Perturbed system 83
Projection matrix 16, ... 

 books.google.com None of the changes was radical, although the important novelty of volume
surface integrals arose in the contributions of Duhamel and especially
Ostrogradsky. Libri and Liouville modified the diffusion equation itself, although
their methods of ... 

 books.google.com equation (2.6) arranged in decreasing order Lyapunov characteristic exponent
spectrum or LCEspectrum of the ... The phase volume time evolution is given by
Ostrogradsky  Liouville formula: t V(t)  V(t0)exp j" SpA(T)dtJ f (2.22) t0 N where ... 

 