SCOPUS 정보 검색 플랫폼

Volumn 162, Issue 1-2, 2002, Pages 34-52

Slow passage through homoclinic orbits for the unfolding of a saddle-center bifurcation and the change in the adiabatic invariant

(2) Diminnie, David C a Haberman, Richard b

a TEXAS INSTRUMENTS (United States)

b SOUTHERN METHODIST UNIVERSITY (United States)

Author keywords

Action; Adiabatic invariants; Average; Homoclinic orbits; Nonlinear dynamical systems; Unfolding of saddle center bifurcation

Indexed keywords

BIFURCATION (MATHEMATICS); DEGREES OF FREEDOM (MECHANICS); DYNAMICS;

ADIABATIC INVARIANT;

HAMILTONIANS;

EID: 0036467598 PISSN: 01672789 EISSN: None Source Type: Journal
DOI: 10.1016/S0167-2789(01)00373-6 Document Type: Article

Times cited : (32)

References (35)

1
- 0004104179
- Springer, New York
- (1999) Chaos Near Resonance
- Haller, G.¹

2
- 0001358427
- The adiabatic invariant in classical mechanics
- C.K.R.T. Jones, U. Kirchgraber, H.O. Walther (Eds.), Springer, New York
- (1993) Dynamics Reported Expositions in Dynamical Systems, New Series , vol.2 , pp. 117-235
- Henrard, J.¹

3
- 0003460866
- Springer, New York
- (1988) Mathematical Aspects of Classical and Celestial Mechanics, Dynamical Systems III
- Arnold, V.I.¹ Kozlov, V.V.² Neishtadt, A.I.³

4
- 33644697094
- Asymptotic theory of Hamiltonian and other systems with all solutions nearly periodic
- (1962) J. Math. Phys. , vol.3 , pp. 806-828
- Kruskal, M.D.¹

5
- 0003957366
- Springer, New York
- (1985) Averaging Methods in Nonlinear Dynamical Systems
- Sanders, J.A.¹ Verhulst, F.²

6
- 0000410999
- Change of an adiabatic invariant at a separatrix
- (1986) J. Plasma Phys. , vol.12 , pp. 568-573
- Neishtadt, A.I.¹

7
- 33750120064
- Adiabatic invariant change due to separatrix crossing
- (1986) Phys. Rev. A , vol.34 , pp. 4256-4275
- Cary, J.R.¹ Escande, D.F.² Tennyson, J.L.³

8
- 0025564810
- Separatrix crossing: Time-invariant potentials with dissipation
- (1990) SIAM J. Appl. Math. , vol.50 , pp. 1716-1744
- Bourland, F.J.¹ Haberman, R.²

9
- 0002965978
- Phase change between separatrix crossings
- (1989) Physica D , vol.36 , pp. 287-316
- Cary, J.R.¹ Skodje, R.T.²

10
- 0000597915
- Chaotic advection in a cubic Stokes flow
- (1998) Physica D , vol.111 , pp. 227-242
- Neishtadt, A.I.¹ Vainshtein, D.L.² Vasiliev, A.A.³

11
- 0038877543
- Changes in the adiabatic invariant and streamline chaos in confined incompressible Stokes flow
- (1996) Chaos , vol.6 , pp. 67-77
- Vainshtein, D.L.¹ Vasiliev, A.A.² Neishtadt, A.I.³

12
- 0003483217
- Springer, New York
- (1985) Singularities and Groups in Bifurcation Theory , vol.1
- Golubitsky, M.¹ Schaeffer, D.G.²

13
- 0003483217
- Springer, New York
- (1988) Singularities and Groups in Bifurcation Theory , vol.2
- Golubitsky, M.¹ Schaeffer, D.G.²

14
- 0003478288
- Springer, New York
- (1983) Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
- Guckenheimer, J.¹ Holmes, P.²

15
- 0003048021
- Moscow State University, English Trans.: Selecta Math. Soviet 1 (4) (1981) 373-388
- (1976) Versal deformations of a singular point on the plane in the case of zero eigenvalues , pp. 37-65
- Bogdanov, R.¹

16
- 51649178043
- Singularities of vector fields
- (1974) Publ. Math. IHES , vol.43 , pp. 47-100
- Takens, F.¹

17
- 0002533366
- Forced oscillations and bifurcation
- (1974) Comm. Math. Inst. Rijksuniversiteit Utrecht , vol.3 , pp. 1-59
- Takens, F.¹

18
- 84956229471
- On the versality of a family of symmetric vector-fields in the plane
- (1984) Math. USSR-Sb. , vol.48 , pp. 463-498
- Zoladek, H.¹

19
- 0002562820
- Bifurcations of certain family of planar vector fields tangent to axes
- (1987) MJ. Diff. Eqns. , vol.67 , pp. 1-55
- Zoladek, H.¹

20
- 0004154138
- Springer, New York
- (1994) Bifurcation Theory and Catastrophe Theory
- Arnold, V.I.¹ Afrajmovich, V.S.² Il'yashenko, Yu.S.³ Shil'nikov, L.P.⁴

21
- 0003687338
- Springer, New York
- (1998) Elements of Applied Bifurcation Theory, 2nd Edition
- Kuznetsov, Y.A.¹

22
- 0016549570
- Exchange of stabilities in autonomous systems
- (1975) Stud. Appl. Math. , vol.54 , pp. 229-260
- Lebovitz, N.R.¹ Schaar, R.J.²

23
- 0001915231
- Exchange of stabilities in autonomous systems. II. Vertical bifurcation
- (1977) Stud. Appl. Math. , vol.56 , pp. 1-50
- Lebovitz, N.R.¹ Schaar, R.J.²

24
- 0000881312
- Persistence of stability loss for dynamical bifurcations I
- (1987) Diff. Eq. , vol.23 , pp. 1385-1391
- Neishtadt, A.I.¹

25
- 0000190869
- Persistence of stability loss for dynamical bifurcations II
- (1988) Diff. Eq. , vol.24 , pp. 171-176
- Neishtadt, A.I.¹

26
- 0018506677
- Slowly varying jump and transition phenomena associated with algebraic bifurcation problems
- (1979) SIAM J. Appl. Math. , vol.37 , pp. 69-106
- Haberman, R.¹

27
- 0030167803
- Slow passage through a pitchfork bifurcation
- (1996) SIAM J. Appl. Math. , vol.56 , pp. 889-918
- Mareé, G.J.M.¹

28
- 0001460135
- Slow passage through a saddle-center bifurcation
- (2000) J. Nonlinear Sci. , vol.10 , pp. 197-221
- Diminnie, D.C.¹ Haberman, R.²

29
- 0034379156
- Slow passage through a transcritical bifurcation for Hamiltonian systems and the change in action due to a nonhyperbolic homoclinic orbit
- (2000) Chaos , vol.10 , pp. 641-648
- Haberman, R.¹

30
- 0036252823
- Slow passage through the nonhyperbolic homoclinic orbit associated with a subcritical pitchfork bifurcation for Hamiltonian systems and the change in action
- (2001) SIAM J. Appl. Math. , vol.62 , pp. 488-513
- Haberman, R.¹

31
- 4243530073
- submitted for publication
- Action and period of homoclinic and periodic orbits for the unfolding of a saddle-center bifurcation
- Diminnie, D.C.¹ Haberman, R.²

32
- 0003528989
- McGraw-Hill, New York
- (1966) Functions of a Complex Variable
- Carrier, G.F.¹ Krook, M.² Pearson, C.E.³

33
- 0004131606
- Academic Press, New York
- (1974) Riemann's Zeta Function
- Edwards, H.M.¹

34
- 0003957510
- Cambridge University Press, Cambridge
- (1969) A Course of Modern Analysis
- Whittaker, E.T.¹ Watson, G.N.²

35
- 0003219756
- The isomonodromic deformation method in the theory of Painlevé equations
- Springer, New York
- (1986) Lecture Notes in Mathematics , vol.1191
- Its, A.R.¹ Novokshenov, V.Y.²

* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.