237 citations · 662 across the 35 of their papers we have counts for
8 papers · 1 filter
Infinite towers in the graph of a dynamical system
Roberto De Leo, James A. Yorke
Chaotic attractors, chaotic saddles and periodic orbits are examples of chain-recurrent sets. Using arbitrary small controls, a trajectory starting from any point in a chain-recurr…
Low-dimensional paradigms for high-dimensional hetero-chaos
Yoshitaka Saiki, Miguel A. F. Sanjuan, James A. Yorke
The dynamics on a chaotic attractor can be quite heterogeneous, being much more unstable in some regions than others. Some regions of a chaotic attractor can be expanding in more d…
The continuous route to multi-chaos
Yoshitaka Saiki, Miguel A. F. Sanjuan, James A. Yorke
For low-dimensional chaotic attractors there is usually a single number of unstable dimensions for all of its periodic orbits and we can say such attractors exhibit "mono-chaos". I…
Partially controlling transient chaos in the Lorenz equations
Rubén Capeáns, Juan Sabuco, Miguel A. F. Sanjuán +1
Transient chaos is a characteristic behavior in nonlinear dynamics where trajectories in a certain region of phase space behave chaotically for a while, before escaping to an exter…
The Scaling of Chaos vs Periodicity: How Certain is it that an Attractor is Chaotic?
Madhura Joglekar, Edward Ott, James A. Yorke
The character of the time-asymptotic evolution of physical systems can have complex, singular behavior with variation of a system parameter, particularly when chaos is involved. A…
Connecting period-doubling cascades to chaos
Evelyn Sander, James A. Yorke
The appearance of infinitely-many period-doubling cascades is one of the most prominent features observed in the study of maps depending on a parameter. They are associated with ch…
The cascades route to chaos
Evelyn Sander, James A. Yorke
The presence of a period-doubling cascade in dynamical systems that depend on a parameter is one of the basic routes to chaos. It is rarely mentioned that there are virtually alway…
Turbulence transition and the edge of chaos in pipe flow
Tobias M Schneider, Bruno Eckhardt, James A Yorke
The linear stability of pipe flow implies that only perturbations of sufficient strength will trigger the transition to turbulence. In order to determine this threshold in perturba…