Zeros of Abelian integrals for a quartic Hamiltonian with figure-of-eight loop through a nilpotent saddle
In this paper, we give the upper bound of the number of zeros of Abelian integral I ( h ) = ∮ Γ h g ( x , y ) d y − f ( x , y ) d x , where Γ h is the closed orbit defined by H ( x , y ) = − x 2 + x 4 + y 4 + r x 2 y 2 = h , r ≥ 0 , r ≠ 2 , h ∈ Σ , Σ is the maximal open interval on which the ovals {...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Yang, Jihua [verfasserIn] |
|---|
| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Umfang: |
16 |
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| Übergeordnetes Werk: |
Enthalten in: Lecithin decorated thin film composite (TFC) nanofiltration membranes for enhanced sieving performance - Cheng, Lilantian ELSEVIER, 2023, Amsterdam [u.a.] |
|---|---|
| Übergeordnetes Werk: |
volume:27 ; year:2016 ; pages:350-365 ; extent:16 |
| Links: |
|---|
| DOI / URN: |
10.1016/j.nonrwa.2015.08.005 |
|---|
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ELV035107928 |
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| 520 | |a In this paper, we give the upper bound of the number of zeros of Abelian integral I ( h ) = ∮ Γ h g ( x , y ) d y − f ( x , y ) d x , where Γ h is the closed orbit defined by H ( x , y ) = − x 2 + x 4 + y 4 + r x 2 y 2 = h , r ≥ 0 , r ≠ 2 , h ∈ Σ , Σ is the maximal open interval on which the ovals { Γ h } exist, f ( x , y ) and g ( x , y ) are real polynomials in x and y of degree at most n . | ||
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10.1016/j.nonrwa.2015.08.005 doi GBVA2016004000030.pica (DE-627)ELV035107928 (ELSEVIER)S1468-1218(15)00106-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 570 VZ 58.11 bkl Yang, Jihua verfasserin aut Zeros of Abelian integrals for a quartic Hamiltonian with figure-of-eight loop through a nilpotent saddle 2016 16 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we give the upper bound of the number of zeros of Abelian integral I ( h ) = ∮ Γ h g ( x , y ) d y − f ( x , y ) d x , where Γ h is the closed orbit defined by H ( x , y ) = − x 2 + x 4 + y 4 + r x 2 y 2 = h , r ≥ 0 , r ≠ 2 , h ∈ Σ , Σ is the maximal open interval on which the ovals { Γ h } exist, f ( x , y ) and g ( x , y ) are real polynomials in x and y of degree at most n . Chebyshev space Elsevier Abelian integral Elsevier Weakened Hilbert’s 16th problem Elsevier Picard–Fuchs equation Elsevier Hamiltonian system Elsevier Zhao, Liqin oth Enthalten in Elsevier Science Cheng, Lilantian ELSEVIER Lecithin decorated thin film composite (TFC) nanofiltration membranes for enhanced sieving performance 2023 Amsterdam [u.a.] (DE-627)ELV009570969 volume:27 year:2016 pages:350-365 extent:16 https://doi.org/10.1016/j.nonrwa.2015.08.005 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 58.11 Mechanische Verfahrenstechnik VZ AR 27 2016 350-365 16 045F 510 |
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10.1016/j.nonrwa.2015.08.005 doi GBVA2016004000030.pica (DE-627)ELV035107928 (ELSEVIER)S1468-1218(15)00106-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 570 VZ 58.11 bkl Yang, Jihua verfasserin aut Zeros of Abelian integrals for a quartic Hamiltonian with figure-of-eight loop through a nilpotent saddle 2016 16 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we give the upper bound of the number of zeros of Abelian integral I ( h ) = ∮ Γ h g ( x , y ) d y − f ( x , y ) d x , where Γ h is the closed orbit defined by H ( x , y ) = − x 2 + x 4 + y 4 + r x 2 y 2 = h , r ≥ 0 , r ≠ 2 , h ∈ Σ , Σ is the maximal open interval on which the ovals { Γ h } exist, f ( x , y ) and g ( x , y ) are real polynomials in x and y of degree at most n . Chebyshev space Elsevier Abelian integral Elsevier Weakened Hilbert’s 16th problem Elsevier Picard–Fuchs equation Elsevier Hamiltonian system Elsevier Zhao, Liqin oth Enthalten in Elsevier Science Cheng, Lilantian ELSEVIER Lecithin decorated thin film composite (TFC) nanofiltration membranes for enhanced sieving performance 2023 Amsterdam [u.a.] (DE-627)ELV009570969 volume:27 year:2016 pages:350-365 extent:16 https://doi.org/10.1016/j.nonrwa.2015.08.005 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 58.11 Mechanische Verfahrenstechnik VZ AR 27 2016 350-365 16 045F 510 |
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10.1016/j.nonrwa.2015.08.005 doi GBVA2016004000030.pica (DE-627)ELV035107928 (ELSEVIER)S1468-1218(15)00106-6 DE-627 ger DE-627 rakwb eng 510 510 DE-600 570 VZ 58.11 bkl Yang, Jihua verfasserin aut Zeros of Abelian integrals for a quartic Hamiltonian with figure-of-eight loop through a nilpotent saddle 2016 16 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier In this paper, we give the upper bound of the number of zeros of Abelian integral I ( h ) = ∮ Γ h g ( x , y ) d y − f ( x , y ) d x , where Γ h is the closed orbit defined by H ( x , y ) = − x 2 + x 4 + y 4 + r x 2 y 2 = h , r ≥ 0 , r ≠ 2 , h ∈ Σ , Σ is the maximal open interval on which the ovals { Γ h } exist, f ( x , y ) and g ( x , y ) are real polynomials in x and y of degree at most n . Chebyshev space Elsevier Abelian integral Elsevier Weakened Hilbert’s 16th problem Elsevier Picard–Fuchs equation Elsevier Hamiltonian system Elsevier Zhao, Liqin oth Enthalten in Elsevier Science Cheng, Lilantian ELSEVIER Lecithin decorated thin film composite (TFC) nanofiltration membranes for enhanced sieving performance 2023 Amsterdam [u.a.] (DE-627)ELV009570969 volume:27 year:2016 pages:350-365 extent:16 https://doi.org/10.1016/j.nonrwa.2015.08.005 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA 58.11 Mechanische Verfahrenstechnik VZ AR 27 2016 350-365 16 045F 510 |
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Zeros of Abelian integrals for a quartic Hamiltonian with figure-of-eight loop through a nilpotent saddle |
| abstract |
In this paper, we give the upper bound of the number of zeros of Abelian integral I ( h ) = ∮ Γ h g ( x , y ) d y − f ( x , y ) d x , where Γ h is the closed orbit defined by H ( x , y ) = − x 2 + x 4 + y 4 + r x 2 y 2 = h , r ≥ 0 , r ≠ 2 , h ∈ Σ , Σ is the maximal open interval on which the ovals { Γ h } exist, f ( x , y ) and g ( x , y ) are real polynomials in x and y of degree at most n . |
| abstractGer |
In this paper, we give the upper bound of the number of zeros of Abelian integral I ( h ) = ∮ Γ h g ( x , y ) d y − f ( x , y ) d x , where Γ h is the closed orbit defined by H ( x , y ) = − x 2 + x 4 + y 4 + r x 2 y 2 = h , r ≥ 0 , r ≠ 2 , h ∈ Σ , Σ is the maximal open interval on which the ovals { Γ h } exist, f ( x , y ) and g ( x , y ) are real polynomials in x and y of degree at most n . |
| abstract_unstemmed |
In this paper, we give the upper bound of the number of zeros of Abelian integral I ( h ) = ∮ Γ h g ( x , y ) d y − f ( x , y ) d x , where Γ h is the closed orbit defined by H ( x , y ) = − x 2 + x 4 + y 4 + r x 2 y 2 = h , r ≥ 0 , r ≠ 2 , h ∈ Σ , Σ is the maximal open interval on which the ovals { Γ h } exist, f ( x , y ) and g ( x , y ) are real polynomials in x and y of degree at most n . |
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10.1016/j.nonrwa.2015.08.005 |
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2024-07-06T16:42:05.537Z |
| _version_ |
1803848647220133888 |
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7.399811 |