Dynamics and Periodic Solutions in Cubic Polynomial Hamiltonian Systems
| Autor: | Dante Carrasco-Olivera, Claudio Vidal |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Equilibrium point
Hamiltonian mechanics Applied Mathematics Dynamics (mechanics) Type (model theory) 01 natural sciences Stability (probability) Hamiltonian system 010101 applied mathematics symbols.namesake Homogeneous 0103 physical sciences symbols Discrete Mathematics and Combinatorics 0101 mathematics 010301 acoustics Cubic function Mathematics Mathematical physics |
| Zdroj: | Qualitative Theory of Dynamical Systems. 18:383-403 |
| ISSN: | 1662-3592 1575-5460 |
| DOI: | 10.1007/s12346-018-0291-2 |
| Popis: | We consider the Hamiltonian function defined by the cubic polynomial H=12(y12+y22)+V(x1,x2) where the potential V(x)=δV2(x1,x2)+V3(x1,x2), with V2(x1,x2)=12(x12+x22) and V3(x1,x2)=13x13+fx1x22+gx23, with f and g are real parameters such that f≠0 and δ is 0 or 1. Our objective is to study the number and bifurcations of the equilibria and its type of stability. Moreover, we obtain the existence of periodic solutions close to some equilibrium points and an isolated symmetric periodic solution distant of the equilibria for some convenient region of the parameters. We point out the role of the parameters and the difference between the homogeneous potential case (δ=0) and the general case (δ=1). |
| Databáze: | OpenAIRE |
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