Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 36 for “"Hamiltonian systems"”.
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Ensemble control of Hamiltonian systems
… tended to make simplifying assumptions on the systems in view, and this paper attempts to remove some of those assumptions. Even in a non-linear ensemble system, it can be demonstrated that controllability is achievable under some circumstances. This controllability is limited, however, by the …
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Spectral Methods For The Hamiltonian Systems
… with some</p> <p>symplectic methods in solving Hamiltonian dynamical systems. Our</p> <p>main emphasis is on the non-linear problems. Numerical evidence has</p> <p>demonstrated that the proposed spectral collocation method preserves</p> <p>both energy and symplectic structure up to the machine …
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Chaotic diffusion in nonlinear Hamiltonian systems
This work investigates diffusion in nonlinear Hamiltonian systems. The diffusion, more precisely subdiffusion, in such systems is induced by the intrinsic chaotic behavior of trajectories and thus is called chaotic diffusion''. Its properties are studied on the example of one- or two-dimensional …
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Nonlinear dynamics and chaos in multidimensional disordered Hamiltonian systems
… study the chaotic behavior of multidimensional Hamiltonian systems in the presence of nonlinearity and disorder. It is known that any localized initial excitation in a large enough linear disordered system spreads for a finite amount of time and then halts forever. This phenomenon is called …
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Monotonicity of the Period Function for Hamiltonian Systems with Potentials
… monotonic behaviour of the period function for Hamiltonian systems with potentials, we denote as oscillators. Departing from traditional methods, we partition each orbit into two segments and analyse the period restricted to these segments. Analogously to the period function, these restrictions …
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Antilinear deformations of Coxeter groups with application to Hamiltonian systems
In this thesis we provide several different systematic methods for constructing complex root spaces that remain invariant under an antilinear transformation. The first method is based on any element of the Weyl group, which is extended to factorizations of the Coxeter element and a reduced Coxeter …
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Stochastically Perturbed Dynamics of Hamiltonian Systems Near 1:1-Resonance
… perturbed two-degrees of freedom integrable systems is emphasized throughout the study. The extension of the method of stochastic averaging on graphs to 1:1-resonant Hamiltonian systems forms the other major aspect of this work.
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Stationary Configurations of Point Vortices (Morse Theory, Hamiltonian Systems, Fluid Mechanics)
… problem of fluid mechanics, which was given a Hamiltonian formulation by Kirchhoff. Stationary configurations are those which remain self-similar throughout the motion, and are of considerable physical interest.
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Application of the Lagrangian descriptors method to Hamiltonian systems with emphasis to models of barred galaxies
… we apply the LDs method to different dynamical systems. We first study a Hamiltonian system of galactic type to highlight normally hyperbolic invariant manifolds (NHIMs), examining the impact of different pattern speeds and energy levels on the NHIMs' structure and determine how these features …
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Canonical integration methods for Hamiltonian dynamical systems
Hamiltonian systems possess dynamics (e.g., preservation of volume in phase space and symplectic structure) that call for special numerical integrators, namely canonical methods. Recent research in this aspect have shown that canonical numerical integrators may be needed for Hamiltonian systems. In …
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Investigating Hamiltonian dynamics by the method of covariant Lyapunov vectors
… investigate the dynamics of several autonomous Hamiltonian systems. The algorithm which we use for computing CLVs is the one developed by Ginelli and collaborators (G&C), which is quite efficient and has been used previously in many numerical investigations. Using two low-dimensional Hamiltonian …
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Método da forma normal e suas aplicações em oscilações e estabilidade
… method for the study of nonlinear systems of ordinary differential equations near an equilibrium point, especially 1n the case of a bifurcation. This method is called "Normal Form Method" (NFM) and it is based in the Normal Form Theory and Center Manifold Theory. We derive recursive …
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Stochastic Geometric Mechanics and Symmetry
… in stochastically perturbed mechanical systems, in Hamiltonian as well as Lagrangian (variational) formulations. On the Hamiltonian side, we discuss a stochastic Kepler problem with a noisy angular momentum vector. We show that the radial distance and speed evolve deterministically. This …
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Equivariant Kolmogorov-Arnold-Moser theory
… certain invariant tori within nearly integrable Hamiltonian systems. The invariant tori are associated with a set of torus frequencies, and a key result in the theory is that these frequencies must satisfy a Diophantine condition, with no rational resonances amongst the frequencies. In this paper …
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Mathematical Tools for Discontinuous Dynamical Systems
Nonsmooth equations and discontinuous dynamical systems can be used to model systems in a variety of applications, including modeling of certain physical systems and optimization problems. However, theoretical results are somewhat limited for these classes of problems, restricting their use in …
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Chaotic transport by a turnstile mechanism in 4D symplectic maps
Many systems in nature, e.g. atoms, molecules and planetary motion, can be described as Hamiltonian systems. In such systems, the transport between different regions of phase space determines some of their most important properties like the stability of the solar system and the rate of chemical …
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Integrabilidad de sistemas no lineales hamiltonianos con N grados de libertad
Esta Tesis presenta nuevos sistemas hamiltonianos clásicos completamente integrables N dimensionales, construidos mediante la técnica de simetría de coálgebra. Primeramente se ha obtenido la condición necesaria de integrabilidad para una representación simpléctica de cualquier coálgebra de Poisson. …
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Finding and exploiting structure in complex systems via geometric and statistical methods
… geometric and statistical techniques to two Hamiltonian systems to find and exploit structure in the phase space that helps us get qualitative and quantitative results about the phase space transport. While the structure can be revealed by the study of invariant manifolds of fixed points and …
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Hamiltonian chaos: from galactic dynamics to plasma physics
… investigation of the influence of chaos in Hamiltonian models describing the behavior of charged particle orbits in plasma, the motion of stars in barred galaxies, and the diffusion of trajectories in multidimensional maps. First, we systematically explore the interplay between magnetic and …
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Memory efficient approaches of second order for optimal control problems
… Furthermore, the concept of symplecticness and Hamiltonian systems is introduced. In this regard, a suitable numerical method is presented, which can be applied to unconstrained optimal control problems. It is proved that this method is a symplectic one. The iterative solution of optimal control …
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