Rayleigh-Beanrd convection is natural convection that appears in a fluid layer with heated bottom and cooled top planes. When the temperature difference is not so large, steady Rayleigh-Benard convection appears in the layer. However, when the Rayleigh number is increased by raising the temperature difference, the velocity fields may perturb slightly by even oscillatory instability. In such flow, some fluid particles may be transported chaotically. In order to clarify the mechanism of chaotic fluid transport in perturbed Rayleigh-Benard convection, we measured the two-dimensional velocity fields of the convection by Particle Image Velocimetry (PIV) and detected the invariant manifolds called the Lagrangian coherent structures (LCSs). It is observed that the LCSs entangle with each other around cell boundaries and create homoclinic tangles. It is implied that the chaotic fluid transport is induced by horseshoe maps. Furthermore, it is observed that a figure-eight structure appears in the middle of each cell. In AY2021, we especially proposed a perturbed Hamiltonian model of the convection which represents the experimental results better.