The maximum value principle plays an important role in the study of a semi-linear system within time domain, and it uses this paper to existence solutions for systems with general non-linear terms.

We establish a “conditional” variational principle, which unifies and extends many results in the multifractal analysis of dynamical systems. Namely, instead of considering several quantities of local nature and studying separately their multifractal spectra we develop a unified approach which allows us to obtain all spectra from a new multifractal spectrum. Using the variational principle we a...

Dynamical simulation models of tree growth and morphology were developed to address questions about the interrelations between tree structure, functions and environmental conditions on a mesoscale level. The modelling approach has a formal basis in stochastic growth grammars (i.e., extended L-systems), which can be interpreted by the software GROGRA (Growth Grammar Interpreter) yielding time se...

‎in this text we prove that in generalized shift dynamical system $(x^gamma,sigma_varphi)$‎ ‎for finite discrete $x$ with at least two elements‎, ‎infinite countable set $gamma$ and‎ ‎arbitrary map $varphi:gammatogamma$‎, ‎the following statements are equivalent‎: ‎ - the dynamical system $(x^gamma,sigma_varphi)$ is‎ li-yorke chaotic;‎ - the dynamical system $(x^gamma,sigma_varphi)$ has‎ an scr...

In this paper, we introduce the concept of dynamical distance on a nuclear conguration space. We partition the nuclear conguration space into disjoint classes. This classification coincides with the classical partitioning of molecular systems via the concept of conjugacy of dynamical systems. It gives a quantitative criterion to distinguish dierent molecular structures.

in this paper, we introduce a notion of property (t) for a c∗-dynamical system (a, g, α) consisting of a unital c∗-algebra a,a locally compact group g, and an action α on a. as a result,we show that if a has strong property (t) and g has kazhdan’sproperty (t), then the triple (a, g, α) has property (t).

In this paper semi-smooth Newton methods for optimal control problems governed by the dynamical Lamé system are considered and their convergence behavior with respect to superlinear convergence is analyzed. Techniques from Kröner, Kunisch, Vexler (2011), where semi-smooth Newton methods for optimal control of the classical wave equation are considered, are transferred to control of the dynamica...

We prove a local variational principle of pressure for any given open cover. More precisely, for a given dynamical system (X,T ), an open cover U of X, and a continuous, realvalued function f on X, we show that the corresponding local pressure P (T, f ;U) satisfies P (T, f ;U) = sup{hμ(T,U) + ∫ X f(x)dμ(x) : μ is a T -invariant measure}, and moreover, the supremum can be attained by a T -invari...