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In the second part of the thesis, we study physical billiards where the moving particle has a finite nonzero size. In contrast to mathematical billiards where a trajectory is excluded when it hits a corner point of the boundary, in physical billiards reflection of the physical particle (a ball) off a visible corner point is well-defined. Initially, we study properties of such reflections in a physical billiards. Our results confirm that the reflection considered in the literature about physical billiards are indeed no-slip friction-free (elastic) collisions.
In the third part of the thesis, we study physical Ehrenfests' wind-tree models, where we show that physical wind-tree models are dynamically richer than the well-known Lorentz gas model. More precisely, when we replace the point particle by a physical one (a ball), the wind-tree models show a new superdiffusive regimes that never been observed in any other model such as Lorentz gas.
Finally, we prove that typical physical polygonal billiard is hyperbolic at least on a subset of positive measure and therefore has a positive Kolmogorov-Sinai entropy for any positive radius of the moving particle.
