Extreme events, such as rogue waves, earthquakes, and stock market crashes, occur
spontaneously in many dynamical systems. Because of their usually adverse …

Dynamical systems and their linear stability; 2. Topological chaos; 3. Liouvillian dynamics; 4.
Probabalistic chaos; 5. Chaotic scattering; 6. Scattering theory of transport; 7. Hydrodynamic …

On the example of the famous Lorenz system, the difficulties and opportunities of reliable
numerical analysis of chaotic dynamical systems are discussed in this article. For the Lorenz …

All biological systems can be classified as open, dissipative and non-linear. This review
introduces the most typical phenomena associated with non-linearity, dissipation and …

Quantum chaos of many-body (MB) systems has been swiftly develo** into a vibrant
research area at the interface between various disciplines, ranging from statistical physics to …

A dynamical systems approach to turbulence envisions the flow as a trajectory through a
high-dimensional state space [Hopf, Commun. Appl. Maths 1, 303 (1948)]. The chaotic …

We give simple conditions that guarantee, for strongly dissipative maps, the existence of
strange attractors with a single direction of instability and certain controlled behaviors. Only …

A chaotic dynamics is typically characterized by the emergence of strange attractors with
their fractal or multifractal structure. On the other hand, chaotic synchronization is a unique …

Despite the nonlinear nature of turbulence, there is evidence that part of the energy-transfer
mechanisms sustaining wall turbulence can be ascribed to linear processes. The different …

Non-periodic solutions are an essential property of chaotic dynamical systems. Simulations
with deterministic finite-precision numbers, however, always yield orbits that are eventually …