Related papers: What make them all so turbulent
We give some basic properties of strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces. Then we present some other results for which our mappings need to be continuous.
An analytic theory is developed for the density of states oscillations in quantum wells in a magnetic field which is tilted with respect to the barrier planes. The main oscillations are found to come from the simplest one or two-bounce…
We study a class of one-dimensional full branch maps admitting two indifferent fixed points as well as critical points and/or unbounded derivative. Under some mild assumptions we prove the existence of a unique invariant mixing absolutely…
We identify a set of quantum graphs with unique and precisely defined spectral properties called {\it regular quantum graphs}. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are…
To each colored graph, one can associate its closure in the universal space of isomorphism classes of pointed colored graphs, and this subspace can be regarded as a generalized subshift. Based on this correspondence, we extend the notion of…
We study a class of chainable continua which contains, among others, all inverse limit spaces generated by a single interval bonding map which is piecewise monotone and locally eventually onto. Such spaces are realized as attractors of…
Transitivity, the existence of periodic points and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that for graphs that are not trees, for every $\varepsilon>0,$ there exist (complicate)…
Many dynamical systems of different complexity, e.g. 1D logistic map, the Lorentz equations, or real phenomena, like turbulent convection, show chaotic behaviour. Despite huge differences, the dynamical scenarios for these systems are…
In many applications, there is a desire to determine if the dynamics of interest are chaotic or not. Since positive Lyapunov exponents are a signature for chaos, they are often used to determine this. Reliable estimates of Lyapunov…
We revisit the globally coupled map lattice (GCML). We show that in the so called turbulent regime various periodic cluster attractor states are formed even though the coupling between the maps are very small relative to the non-linearity…
In the turbulent regime of coupled map lattice with non-local interaction the maps systematically form periodic cluster attractors and their remnants by synchronization due to the foliation of periodic windows of the element map. We examine…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
Numerical analysis indicates that there exists an unexpected new ordered chaos for the bounded one-dimensional multibarrier potential. For certain values of the number of barriers, repeated identical forms (periods) of the wavepackets…
We show that the output of systems with time-varying delay can exhibit a new kind of chaotic behavior characterized by laminar phases, which are periodically interrupted by irregular bursts. Within each laminar phase the output intensity…
From a two-agent, two-strategy congestion game where both agents apply the multiplicative weights update algorithm, we obtain a two-parameter family of maps of the unit square to itself. Interesting dynamics arise on the invariant diagonal,…
Very little is currently known about the dynamics of non-polynomial entire maps in several complex variables. The family of transcendental H\'enon maps offers the potential of combining ideas from transcendental dynamics in one variable,…
In this paper, we are concerned with the existence of invariant curves of the planar twist mappings where the perturbations are almost periodic. As an application, the existence of almost periodic solutions and the boundedness of all…
In the theory of renormalization for classical dynamical systems, e.g. unimodal maps and critical circle maps, topological conjugacy classes are stable manifolds of renormalization. Physically more realistic systems on the other hand may…
In a generic dynamical system chaos and regular motion coexist side by side, in different parts of the phase space. The border between these, where trajectories are neither unstable nor stable but of marginal stability, manifests itself…
By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…