Global Dynamics of Planar Piecewise Linear Inelastic systems having straight lines as switching manifolds

Villanueva, Y.; Euzébio, R.D.

doi:10.1016/j.nonrwa.2023.103994

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Introduction and Statement Of The Main Results1

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2024

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“…[9] for the index theory of the piecewise models, ref. [10] for the global dynamics of some piecewise models, ref. [11] for a center problem in piecewise models, ref.…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

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Limit Cycles of Discontinuous Piecewise Differential Hamiltonian Systems Separated by a Straight Line

Casimiro,

Llibre

2024

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In this article, we study the maximum number of limit cycles of discontinuous piecewise differential systems, formed by two Hamiltonians systems separated by a straight line. We consider three cases, when both Hamiltonians systems in each side of the discontinuity line have simultaneously degree one, two or three. We obtain that in these three cases, this maximum number is zero, one and three, respectively. Moreover, we prove that there are discontinuous piecewise differential systems realizing these maximum number of limit cycles. Note that we have solved the extension of the 16th Hilbert problem about the maximum number of limit cycles that these three classes of discontinuous piecewise differential systems separated by one straight line and formed by two Hamiltonian systems with a degree either one, two, or three, which such systems can exhibit.

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“…[9] for the index theory of the piecewise models, ref. [10] for the global dynamics of some piecewise models, ref. [11] for a center problem in piecewise models, ref.…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 99%

“…respectively. The Hamiltonians H 1 (x, y) and H 2 (x, y) are first integrals of systems ( 9) and (10), respectively. Now, we look for the limit cycles that intersect the straight line x = 0 at the points (0, y 1 ) and (0, y 2 ), with y 1 ̸ = y 2 .…”

Section: Proof Of Statement (C)mentioning

confidence: 99%

Limit Cycles of Discontinuous Piecewise Differential Hamiltonian Systems Separated by a Straight Line

Casimiro,

Llibre

2024

Axioms

View full text Add to dashboard Cite

show abstract

Global Dynamics of Planar Piecewise Linear Inelastic systems having straight lines as switching manifolds

Cited by 1 publication

References 6 publications

Limit Cycles of Discontinuous Piecewise Differential Hamiltonian Systems Separated by a Straight Line

Limit Cycles of Discontinuous Piecewise Differential Hamiltonian Systems Separated by a Straight Line

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