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In this survey, we provide a concise introduction to convex billiards and describe some recent results, obtained by the authors… Expand We study distributions of the ratios of level spacings of rectangular and Africa-shaped superconducting microwave resonators… Expand Experiments with superconducting microwave cavities have been performed in our laboratory for more than two decades. The purpose… Expand Motivated by recent experimental observations of size quantization of electron energy levels in graphene quantum dots  we… Expand Two area-preserving twist maps are associated to a smooth closed convex table: the (classical) billiard map and the dual billiard… Expand Wave functions of pseudointegrable plane polygonal billiards are investigated. It is demonstrated that they have clear structures… Expand The plane wave decomposition method (PWDM) is one of the most popular strategies for numerical solution of the quantum billiard… Expand A detail study of the diffusive and heat conduction properties of a family of nonchaotic billiards is presented. For dynamical… Expand Abstract:We propose a plasma model for spectral statistics displaying level repulsion without long-range spectral rigidity, i.e… Expand We discuss gravitational billiards, i.e. the two-dimensional motion of a paint mass inside a hard boundary curve under the… Expand