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In this paper, we consider horseshoe motion in the planar restricted threebody problem. On one hand, we deal with the families of horseshoe periodic orbits (HPOs) (which surround three equilibrium points called L 3 , L 4 and L 5 ), when the mass parameter µ is positive and small; we describe the structure of such families from the two-body problem (µ = 0). On the other hand, the region of existence of HPOs for any value of µ ∈ (0, 1/2] implies the understanding of the behaviour of the invariant manifolds of L 3 . So, a systematic analysis of such manifolds is carried out. As well the implications on the number of homoclinic connections to L 3 and on the simple infinite and double infinite period homoclinic phenomena are analysed. Finally, the relationship between the horseshoe homoclinic orbits and the HPO is considered in detail.

Experimental results of the hydrostatic pressure influence on Mössbauer spectrum parameters are obtained over the pressure range including the area of structural phase transition. A linear increase of the Mössbauer effect probability (recoilless fraction) is accompanied by a linear decrease of the electron density at tin nuclei within the pressure range foregoing the phase transition. The electric resistance and the recoilless fraction of the new phase of Mg2Sn are lower, but the electron density at tin nuclei is greater than the initial phase ones. Hydrostatic conditions allow to fix clearly the diphasic transition area and to determine the influence of the pressure on the Mössbauer line position and on the recoilless fraction of the high pressure phase. The phase transition heat Q = 415 cal mol−1 is calculated using recoilless fractions of the high and low pressure phases at 25 kbar. The present results are qualitatively and quantitatively different from the results, obtained at nonhydrostatic conditions.

Experimental results reflect a linear increase of the recoilless fraction and a linear decrease of the electron density at the tin nuclei of SnTe with increasing pressure to 16 kbar. Beginning with 16 kbar the appearance of the high pressure phase is observed, the recoilless fraction of which is greater and the electron density at the tin nuclei is less than the low pressure phase ones. For powdered and single crystal specimens the phase transition is accompanied by a large two‐phase region. The result of the recoilless fraction change are used for the calculation of the phase‐transition heat and the slope of the equilibrium line.

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