Preface; Contents; 1 Solvability of Some Integro-Differential Equations with Anomalous Diffusion; 1.1 Introduction; 1.2 The Existence of the Perturbed Solution; 1.3 The Continuity of the Fixed Point of the Map Tg; 1.4 Auxiliary Results; References; 2 Poincaré Recurrences in Ergodic Systems Without Mixing; 2.1 Introduction; 2.2 Model Under Study; 2.3 Main Properties of Return Time Dependence for the Linear Circle Map; 2.4 Afraimovich
Pesin Dimension for Different Rotation Numbers; 2.5 Impact of Nonlinearity

2.6 Fibonacci Stairs and the Afraimovich
Pesin Dimension for a Stroboscopic Section of a Nonautonomous van der Pol Oscillator2.6.1 System Under Study; 2.6.2 Numerical Results; 2.7 Poincaré Recurrences in Hamiltonian Systems; 2.7.1 Poincaré Recurrences in a Periodically Driven Nonlinear Conservative Oscillator; 2.8 Conclusion; References; 3 Success, Hierarchy, and Inequality Under Uncertainty; 3.1 Introduction; 3.2 Enhancing Success Chances by Persistent Learning and Skill Acquisition; 3.3 Like a Squirrel in a Wheel
Freud's Repetition Compulsion; 3.4 The Rich Get Richer
Pareto Principle

3.5 Inequality Rising from Risk Taking Under Uncertainty3.6 Generalized Mass-Action Principle
Emergence of Hierarchies Under Uncertainty; 3.7 Inverse Mass-Action Principle
Inequality Due to Uniqueness and Scarcity; 3.8 Cross-Database Analysis Suggests the Worldwide Growth-Inequality Relation (U-Curve); 3.9 Conclusion; References; 4 Functional Differential Equations with Piecewise Constant Argument; 4.1 Introduction and Preliminaries; 4.2 Retarded Functional Differential Equations with Retarded Constancy of Argument

4.3 Retarded Functional Differential Equations with Alternate Constancy of Argument4.4 Quasilinear Systems: Preliminaries; 4.5 Bounded Solutions of Quasilinear Systems; 4.5.1 Periodic Solutions; 4.5.2 Almost Periodic Solutions; 4.5.3 Examples; 4.6 Further Investigations; References; 5 Grazing in Impulsive Differential Equations; 5.1 Introduction; 5.2 Discontinuous Dynamical Systems; 5.2.1 B-Equivalence to a System with Fixed Moments of Impulses; 5.2.2 Linearization Around Grazing Orbits and Discontinuous Dynamics; 5.2.3 Orbital Stability

5.2.4 Small Parameter Analysis and Grazing Bifurcation5.3 The Grazing Solutions of Non-autonomous Systems with Stationary Impulsive Conditions; 5.3.1 B-Equivalence; 5.3.2 Variational System for Grazing Solutions; 5.3.3 Stability of Grazing Periodic Solutions; 5.3.4 Regular Perturbations Around the Grazing Periodic Solution; 5.4 Conclusion; References; 6 On Local Topological Classification of Two-Dimensional Orientable, Non-Orientable, and Half-Orientable Horseshoes; 6.1 Introduction; 6.2 Linear Smale Horseshoes and Their Boundary Points