Lectures on Geometry of Monge–Ampère Equations with Maple

Entropy in Thermodynamics: from Foliation to Categorization

“…Symmetries of contact structure are such transformations that preserve the Cartan distribution [11], [12]. For a diffeomorphism φ : J 1 (N ) → J 1 (N ) the following condition ensures that it is a contact symmetry:…”

“…J 1 (N ) is sufficient for thermodynamics, however for general theory of jet spaces consult [10], [11], [12].…”

“…We finish this overview of differential geometry by discussing the rudiments of jet spaces. This presentation is mainly based on [11], [12].…”

On symmetry reduction and some classes of invariant solutions of the (1+3)-dimensional homogeneous Monge-Ampère equation

“…has reduced to the investigation of the Monge-Ampère equations in the spaces of different dimensions and different types. Some details on this theme can be found in [33,1,34,37,38,24,21,26,39,22,2,15,40,25,36,23,35] (see, also, the references therein).…”

On Symmetry Reduction of the (1 + 3)-Dimensional Inhomogeneous Monge-Ampère Equation to the First-Order ODEs

“…is reduced to the investigation of the Monge-Ampère equations in the spaces of different dimensions and different types. Some details on this theme can be found in [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] (see, also, the references therein).…”