This paper introduces new invariants for multiparameter dynamical systems. This is done by counting the number of points whose orbits intersect at time n under simultaneous iteration of finitely many ...

Dynamical systems are mathematical models that describe how a point in a given space evolves over time according to a set of rules. Discontinuous dynamics, a subfield of dynamical systems, deals with ...

Proceedings of the American Mathematical Society, Vol. 110, No. 1 (Sep., 1990), pp. 263-268 (6 pages) Two fixed points of a topological dynamical system are said to be of the same type if there exists ...

Dynamical systems theory provides a unifying mathematical framework for understanding how complex phenomena evolve over time. By employing differential and difference equations, researchers can ...

Advanced space travel relies on a fundamental understanding of the restricted three-body problem (RTBP), in which one of the three bodies—typically a spacecraft—is so small that its gravity doesn't ...

Scientists usually use a hypergraph model to predict dynamic behaviors. But the opposite problem is interesting, too. What if researchers can observe the dynamics but don't have access to a reliable ...