One-dimensional Functional Equations

1 Implicit Functions. - 1. 1 Formal solvability. - 1. 2 Theorem on local solvability. - 1. 3 Transformations of equations. - 1. 4 Global solvability. - 1. 5 Comments and references. - 2 Classification of One-dimensional Mappings. - 2. 1 Wandering and non-wandering subsets. - 2. 2 Mappings with wandering compact sets. - 2. 3 Local structure of mappings at an isolated fixed point. - 2. 4 Diffeomorphisms with isolated fixed points. - 2. 5 One-dimensional flows and vector fields. - 2. 6 Embedding problem and iterative roots. - 2. 7 Comments and references. - 3 Generalized Abel Equation. - 3. 1 Local solvability. - 3. 2 Global solutions of equations with not more than one fixed point. - 3. 3 Gluing method for linear equations with several fixed points. - 3. 4 Comments and references. - 4 Equations with Several Transformations of Argument. - 4. 1 Local solvability. - 4. 2 Extension of solutions. - 4. 3 Examples. - 4. 4 Difference equations in Carleman classes. - 4. 5 Comments and references. - 5 Linear Equations. - 5. 1 Generalized linear Abel equation. - 5. 2 Localization of obstacles to solvability. - 5. 3 Equations with constant coefficients. - 5. 4 Equation with affine transformations of argument. - 5. 5 Comments and references.