In addition to the striking beauty inherent in their complex nature, fractals have become a
fundamental ingredient of nonlinear dynamics and chaos theory since they were defined in …

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 …

The emergence of mental states from neural states by partitioning the neural phase space is
analyzed in terms of symbolic dynamics. Well-defined mental states provide contexts …

Metric properties of invariant chaotic sets, like chaotic attractors, are closely related to the
structure of the unstable periodic orbits embedded in this set. As a system parameter is …

A characteristic feature of complex systems is their deep structure, meaning that the
definition of their states and observables depends on the level, or the scale, at which the …

Complex dynamical systems with many degrees of freedom may exhibit a wealth of
collective phenomena related to high-dimensional chaos. This paper focuses on a lattice of …

Two key concepts of quantum theory, complementarity and entanglement, are considered
with respect to their significance in and beyond physics. An axiomatically formalized, weak …

The predictability of an orbit is a key issue when a physical model has strong sensitivity to
the initial conditions and it is solved numerically. How close the computed chaotic orbits are …

Unstable dimension variability is an extreme form of non-hyperbolic behavior that causes a
severe shadowing breakdown of chaotic trajectories. This phenomenon can occur in …

Many chaotic dynamical systems of physical interest present a strong form of
nonhyperbolicity called unstable dimension variability (UDV), for which the chaotic invariant …