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Stabilization of Hamiltonian systems [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 1986 1. HAMILTONIAN SYSTEMS IN THIS paper we will be concerned with the stabilization by feedback of Hamiltonian systems. In order to facilitate our discussions (especially when applying Lyapunov’s second method) we will restrict ourselves to a particular, although natural, subclass of Hamiltonian systems given in the following way [l].
Arjan van der Schaft
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Ergodicity in Hamiltonian systems [PDF]
, 1992 We discuss the Sinai method of proving ergodicity of a discontinuous Hamiltonian system with (non-uniform) hyperbolic behavior.
Carlangelo Liverani +1 more
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AIMS Mathematics, 2023 The discussion of disordered Keplerian Hamiltonian systems in our previously published study, which we verified, is expanded upon in this article. The collision semicircular orbit, and at least one other symmetric orbit is mentioned in this article.
Riadh Chteoui
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Real Hamiltonian forms of Hamiltonian systems [PDF]
The European Physical Journal B, 2004 We introduce the notion of a real form of a Hamiltonian dynamical system in analogy with the notion of real forms for simple Lie algebras. This is done by restricting the complexified initial dynamical system to the fixed point set of a given involution. The resulting subspace is isomorphic (but not symplectomorphic) to the initial phase space. Thus to
G. MARMO +3 more
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Contact Hamiltonian systems [PDF]
Journal of Mathematical Physics, 2019 In this paper, we study Hamiltonian systems on contact manifolds, which is an appropriate scenario to discuss dissipative systems. We show how the dissipative dynamics can be interpreted as a Legendrian submanifold, and also prove a coisotropic reduction theorem similar to the one in symplectic mechanics; as a consequence, we get a method to reduce the
Lainz Valcázar, Manuel +1 more
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Brake orbits with minimal period estimates of first-order variant subquadratic Hamiltonian systems
Electronic Research Archive, 2022 Under a generalized subquadratic growth condition, brake orbits are guaranteed via the homological link theorem. Moreover, the minimal period estimate is given by Morse index estimate and $ L_{0} $-index estimate.
Xiaofei Zhang, Fanjing Wang
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ON THE SYMMETRIES OF HAMILTONIAN SYSTEMS [PDF]
International Journal of Modern Physics A, 1995 In this paper we show how the well-known local symmetries of Lagrangian systems, and in particular the diffeomorphism invariance, emerge in the Hamiltonian formulation. We show that only the constraints which are linear in the momenta generate transformations which correspond to symmetries of the corresponding Lagrangian system.
Andreas Wipf, Viatcheslav Mukhanov
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AIMS Mathematics, 2023 The paper considers the Hamiltonian structure and develops efficient energy-preserving schemes for the nonlinear wave equation with a fractional Laplacian operator. To this end, we first derive the Hamiltonian form of the equation by using the fractional
Tingting Ma , Yuehua He
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Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System
Entropy, 2021 In this paper, a three-terminal memristor is constructed and studied through changing dual-port output instead of one-port. A new conservative memristor-based chaotic system is built by embedding this three-terminal memristor into a newly proposed four ...
Ze Wang, Guoyuan Qi
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Sections of Hamiltonian Systems [PDF]
Regular and Chaotic Dynamics, 2021 A section of a Hamiltonian system is a hypersurface in the phase space of the system, usually representing a set of one-sided constraints (e.g. a boundary, an obstacle or a set of admissible states). In this paper we give local classification results for all typical singularities of sections of regular (non-singular) Hamiltonian systems, a problem ...
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