1 INTRODUCTION  
2 THE RECONSTRUCTION METHOD  
2.1 The extended Fast Action Minimization (eFAM) method  
2.2 Orbits parametrization in generic cosmology  
2.3 Redshift-space  
2.4 Minimization procedure and first guess  
3 BAO RECONSTRUCTION  
3.1 DEUS Full Universe Run haloes  
3.2 Gravitational tidal-field  
4 FITTING THE ACOUSTIC FEATURE  
4.1 Measuring, modeling, and fitting the correlation function  
4.2 Monopole in real space  
4.3 Recovering the BAO signal in statistically anomalous samples  
4.4 RSD modeling: consistency tests  
4.5 Monopole, quadrupole, and anisotropic correlation function in redshift-space  
5 CONCLUSIONS