Finite-time blow-up in dynamical systems
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On bounded and unbounded dynamics of the Hamiltonian system for unified scalar field cosmology
2016, Physics Letters, Section A: General, Atomic and Solid State PhysicsCitation Excerpt :This problem is nontrivial for Hamiltonian systems because these systems preserve phase volumes and, as a result, it is difficult to derive conclusions on the existence of unbounded domains filled by unbounded dynamics only. It is worth to mention that unbounded dynamics studies of nonlinear systems draw attention of many researchers during the last decades, see e.g. works concerning unbounded dynamics of Rössler system; Rikitake system; robust unbounded attractors; open integrable Hamiltonian systems; in the context of proofs of nondissipativity in the sense of Levinson for the phase flow, using Poincaré compactification, analysis of trajectories with finite-time blow-ups and other topics, see e.g. [1,5–8,12,18]. For Hamiltonian systems with more than one degree of freedom their dynamics may vary significantly for different level surfaces.
Theoretical analysis for blow-up behaviors of differential equations with piecewise constant arguments
2016, Applied Mathematics and ComputationPeriodic orbits and 10 cases of unbounded dynamics for one Hamiltonian system defined by the conformally coupled field
2015, Physics Letters, Section A: General, Atomic and Solid State PhysicsCitation Excerpt :Finding nonexistence conditions of compact invariant sets is of considerable interest in the analysis of unbounded dynamics. It is worth to mention that unbounded dynamics studies of nonlinear systems draw attention of many authors during the last decades in the context of proofs of nondissipativity in the Levinson sense of the phase flow, using Poincaré compactification, analysis of trajectories with finite-time blow-ups and other topics, see e.g. [1–6,10,11,20]. In Hamiltonian systems with more than one degree of freedom their dynamics may substantially differs in different level surfaces.
Unbounded trajectories of dynamical systems
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