Surfaces | Dynamical systems

Translation surface

In mathematics a translation surface is a surface obtained from identifying the sides of a polygon in the Euclidean plane by translations. An equivalent definition is a Riemann surface together with a holomorphic 1-form. These surfaces arise in dynamical systems where they can be used to model billiards, and in Teichmüller theory. A particularly interesting subclass is that of Veech surfaces (named after William A. Veech) which are the most symmetric ones. (Wikipedia).

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This video defines a cylindrical surface and explains how to graph a cylindrical surface. http://mathispower4u.yolasite.com/

From playlist Quadric, Surfaces, Cylindrical Coordinates and Spherical Coordinates

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From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications

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From playlist Transformations

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From playlist The Riemann Sphere

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From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications

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From playlist Mathematics

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Modular group | Differential form | Dynamical system | Fiber bundle | Lattice (discrete subgroup) | Interval exchange transformation | Permutation | Thurston boundary | Euler's formula | Bers slice | Fuchsian group | Quadratic differential | Riemann surface | Mathematics | Removable singularity | Euclidean plane | Quasiconformal mapping | Riemann–Roch theorem | Poincaré map | Partition (number theory) | Flow (mathematics) | Moduli space | Fundamental domain | Dynamical billiards | Branched covering | Commensurability (group theory)