Long Distance Propagation of HF Radio Waves

Gurevich, A. V.; Tsedilina, E. E.

doi:10.1007/978-3-642-70249-5

Cited by 35 publications

(38 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Hamiltonian systems with fast and slow variables [1,2,3]. One degree of freedom corresponds to fast variables, and the other corresponds to slow variables.…”

Section: Introductionmentioning

confidence: 99%

“…Let B ν (Î) ∈ P sl be a curve (see (2)) corresponding toÎ such that I ∈ Ξ. According to B), B ν (Î) is divided by Γ(h 0 ) into two parts.…”

mentioning

confidence: 99%

“…LetĴ (2) , ψ (2) denote the values ofĴ , ψ at this time moment. Then the phase point approaches the separatrix again, crosses it and gets captured into G l , l = 1 or l = 2.…”

mentioning

confidence: 99%

“…Then the phase point approaches the separatrix again, crosses it and gets captured into G l , l = 1 or l = 2. Let E = h (2) at the first crossing of the Cq-axis in G l near C. This crossing occurs at time τ = τ − + T 0 + Ø(ε), where T 0 is the slow time period of motion along the trajectoryÎ =Î (0) in the adiabatic approximation. We introduce η (2) = 1 − |h (2) /εΘ − | .…”

mentioning

confidence: 99%

“…For a one has a = 1/ √ −g, where g is the Hessian of E at the point C. The values d 1,2 are defined as the main terms of the expansions (cf. [16])…”

mentioning

confidence: 99%

See 4 more Smart Citations

Stability islands in domains of separatrix crossings in slow-fast Hamiltonian systems

Vasiliev

Neishtadt

Simó

et al. 2007

Proc. Steklov Inst. Math.

View full text Add to dashboard Cite

We consider a 2 d.o.f. Hamiltonian system with one degree of freedom corresponding to fast motion and the other corresponding to slow motion. The ratio of the time derivatives of slow and fast variables is of order 0 < ε ≪ 1. At frozen values of the slow variables there is a separatrix on the phase plane of the fast variables and there is a region in the phase space (the domain of separatrix crossings) where the projections of phase points onto the plane of the fast variables repeatedly cross the separatrix in the process of evolution of the slow variables. Under a certain symmetry condition we prove existence of many (of order 1/ε) stable periodic trajectories in the domain of the separatrix crossings. Each of these trajectories is surrounded by a stability island whose measure is estimated from below by a value of order ε. Thus, the total measure of the stability islands is estimated from below by a value independent of ε. The proof is based on an analysis of the asymptotic formulas for the corresponding Poincaré map.

show abstract

“…Hamiltonian systems with fast and slow variables [1,2,3]. One degree of freedom corresponds to fast variables, and the other corresponds to slow variables.…”

Section: Introductionmentioning

confidence: 99%

“…Let B ν (Î) ∈ P sl be a curve (see (2)) corresponding toÎ such that I ∈ Ξ. According to B), B ν (Î) is divided by Γ(h 0 ) into two parts.…”

mentioning

confidence: 99%

“…LetĴ (2) , ψ (2) denote the values ofĴ , ψ at this time moment. Then the phase point approaches the separatrix again, crosses it and gets captured into G l , l = 1 or l = 2.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

“…For a one has a = 1/ √ −g, where g is the Hessian of E at the point C. The values d 1,2 are defined as the main terms of the expansions (cf. [16])…”

mentioning

confidence: 99%

See 3 more Smart Citations