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Showing 1 to 16 of 16 for “"invariant sets"”.
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Lyapunov Exponents and Invariant Manifold for Random Dynamical Systems in a Banach Space
… the Lyapunov exponents and their associated invariant subspaces for infinite dimensional random dynamical systems in a Banach space, which are generated by, for example, stochastic or random partial differential equations. We prove a multiplicative ergodic theorem. Then, we use this theorem …
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Optimizing model predictive control of processes for wide ranges of operating conditions
… In addition to this, the robustly feasible invariant sets in the state space are calculated off-line and the initial states need to stay inside those invariant sets in order to achieve feasible control operation. The computation of RFMPC is very demanding and computing time is reduced by …
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Dimensions of Self-Similar Fractals
… dimensions of self-similar fractals that are the invariant sets of iterated function systems. We start with the Contraction Mapping Theorem, which will give us a constructive method in which to find fractals using iterated function systems. We then define the Hausdorff metric in order to use the …
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Nontrivial solutions for nonlinear discrete boundary value problems of the fourth order
… pass lemma and a result from the theory of invariant sets of descending flow.
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Exact coherent structures in spatiotemporal chaos: From qualitative description to quantitative predictions
… governing dynamical equations, is shaped by the invariant sets such as equilibria, periodic orbits, and invariant tori. State space of partial differential equations is infinite dimensional, nevertheless, recent computational advancements allow us to find their invariant solutions (exact coherent …
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Passivity Methods for the Stabilization of Closed Sets in Nonlinear Control Systems
… this thesis we study the stabilization of closed sets for passive nonlinear control systems, developing necessary and sufficient conditions under which a passivity-based feedback stabilizes a given goal set. The development of this result takes us to a journey through the so-called reduction …
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Safe trajectory planning of autonomous vehicles
… architecture that combines several linear time-invariant modes with a discrete set of agile maneuvers. The latter are represented by affine transformations in the state space and can be described using a limited number of parameters. We specialize the approach to the case of a small-scale …
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Chaos in Pulsed Laminar Flow
… system with no lower order fixed points, almost invariant sets are natural objects on which to apply the TNCT. In addition, a method is presented to compute line stretching by tracking appropriate motion of finite size rods. This method accounts for the effect of the rod size in computing the …
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Finding and exploiting structure in complex systems via geometric and statistical methods
… the structure can be revealed by the study of invariant manifolds of fixed points and periodic orbits in the first system, there do not exist any fixed points (and hence invariant manifolds) in the second system. The use of statistical (or measure theoretic) and topological methods reveals the …
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Study of the dynamics of transport and mixing using set oriented methods
… using the braids formed by Almost Cyclic Sets (ACS) in certain periodic Stokes' flows. These ACS are closely related to Almost Invariant Sets (AIS) which are identified using a probabilistic set oriented method that makes use of the descritised Perron-Frobenius operator of the flow map. …
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Partially Hyperbolic Systems: Closed Periodic Curves and Closed Orbits
… dynamically coherent. Quite commonly, important invariant sets of regularity no more than C 0 appear in the study of dynamical systems whose regularity is C 1 or better. Seeing as periodic orbits play an important role, we wonder whether a continuous embedded (possibly non differentiable) closed …
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Investigating the infinite spider's web in complex dynamics
… topological and geometric properties of certain invariant sets in the dynamics of entire functions, inspired by recent work of Rippon and Stallard. First, we explore the intricate structure of the spider's web fast escaping sets associated with certain transcendental entire functions. Our results …
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Topological chaos and chaotic mixing of viscous flows
… the flow, invariance or leakiness of the Almost Invariant Sets (AIS) playing the role of ghost rods is found to be in a direct relationship with the rate of homogenization of a scalar. The mixing caused by these AIS and the variations of their structure are explained from the point of view of …
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Quasistationarität und fast-invariante Mengen gewöhnlicher Differentialgleichungen
… due to Fraser and Roussel who approximate an invariant manifold for a reduction of the differential equation. Their original system is in standard form for application of singular perturbation theory. Chapter 2 concludes with the methods of Heinrich and Schauer (resp. Stiefenhofer) for …
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Mathematical approaches to modelling and controlling blood thrombin formation
Chapter 1 is a brief description of the blood coagulation system. Besides making an excursion through the nomenclature and the principal properties, we are confronted with the pertinence of questions that are in nowadays object of discussion among the scientific community investigating the process …