Table 1: Values of the fraction $\xi _{1}(\Lambda =0)/\xi _{1}(\Lambda \neq 0)$ for different values of the ratio $\zeta _{\rm c}$ and the polytropic index. The horizontal lines represents the non well defined radius.
$\zeta _{\rm c}$ n=1 n=3/2 n=2 n=3 n=4 n=5

0.1 $\sim$ 0.88 - - - - -

0.005 $\sim$ 1 $\sim$ 1 $\sim$ 0.98 $\sim$ 0.86 - -

$2\times 10^{-4}$ $\sim$ 1 $\sim$ 1 $\sim$ 1 $\sim$ 1 $\sim$ 0.88 -

$1.2\times 10^{-5}$ $\sim$ 1 $\sim$ 1 $\sim$ 1 $\sim$ 1 $\sim$ 1 -

$6.1\times 10^{-7}$ $\sim$ 1 $\sim$ 1 $\sim$ 1 $\sim$ 1 $\sim$ 1 $\infty$

**Table 1:** Values of the fraction $\xi _{1}(\Lambda =0)/\xi _{1}(\Lambda \neq 0)$ for different values of the ratio $\zeta _{\rm c}$ and the polytropic index. The horizontal lines represents the non well defined radius.
$\zeta _{\rm c}$	n=1	n=3/2	n=2	n=3	n=4	n=5
0.1	$\sim$ 0.88	-	-	-	-	-
0.005	$\sim$ 1	$\sim$ 1	$\sim$ 0.98	$\sim$ 0.86	-	-
$2\times 10^{-4}$	$\sim$ 1	$\sim$ 1	$\sim$ 1	$\sim$ 1	$\sim$ 0.88	-
$1.2\times 10^{-5}$	$\sim$ 1	$\sim$ 1	$\sim$ 1	$\sim$ 1	$\sim$ 1	-
$6.1\times 10^{-7}$	$\sim$ 1	$\sim$ 1	$\sim$ 1	$\sim$ 1	$\sim$ 1	$\infty$

Source LaTeX | All tables | In the text

	1 Introduction
	2 Local dynamics with cosmological constant
	3 Spherical configurations
	4 Nonspherical configurations
	5 Small oscillations in the Newton-Hooke spacetime
	6 Conclusions
	Appendix A
	References