Thermodynamic Formalism for Dispersing Billiards

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Banach Spaces and Thermodynamic Formalism

Introduces Banach spaces for maximal entropy in billiard maps, discussing spectral bounds, norms, and measure construction.

Thermodynamic Formalism for Dispersing Billiards

Explores the geometry and statistical properties of dispersing billiards, aiming to extend the analysis to equilibrium states and covering topics like hyperbolicity and distortion control.

Algebraic Curves: Normalization

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Geometric Potentials and Thermodynamic Formalism

Explores geometric potentials, equilibrium states, and topological pressure in dispersing billiard maps.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Entropy and the Second Law of Thermodynamics

Covers entropy, its definition, and its implications in thermodynamics.

FK-Percolation and the Six-Vertex Model: Critical Phenomena

Covers the transition from the six-vertex model to FK-percolation, focusing on critical phenomena and phase transitions in two-dimensional systems.

Smooth Dynamics: Bernoulli and K Properties

Explores Bernoulli and K properties in smooth dynamics, including equivalence, examples, and implications.

Plane Curves: Singular Points and Multiplicities

Explores plane curves, focusing on singular points, multiplicities, and tangent lines.

Ergodic properties of low complexity symbolic systems

Explores the influence of complexity on ergodic properties of symbolic systems, presenting the Curtis-Hedlund-Lyndon Theorem and constructions of minimal subshifts.