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Volumn 28, Issue 4, 1997, Pages 655-671

Chaos in singular impulsive O.D.E

Author keywords

Melnikov functions; Transversal homoclinic orbits

Indexed keywords

CHAOS THEORY; FUNCTIONS; LINEARIZATION; LYAPUNOV METHODS; PERTURBATION TECHNIQUES; PROBLEM SOLVING; THEOREM PROVING;

EID: 0041726910     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0362-546X(95)00182-U     Document Type: Article
Times cited : (14)

References (15)
  • 1
    • 84968514104 scopus 로고
    • Differentiable dynamical systems
    • SMALE S., Differentiable dynamical systems, Bull. Am. math. Soc. 73, 747-817 (1967).
    • (1967) Bull. Am. Math. Soc. , vol.73 , pp. 747-817
    • Smale, S.1
  • 3
    • 38249016487 scopus 로고
    • Exponential dichotomies, heteroclinic orbits, and Melnikov functions
    • BATTELLI F. & LAZZARI C., Exponential dichotomies, heteroclinic orbits, and Melnikov functions, J. diff. Eqns 86, 342-366 (1990).
    • (1990) J. Diff. Eqns , vol.86 , pp. 342-366
    • Battelli, F.1    Lazzari, C.2
  • 4
    • 85025784004 scopus 로고
    • An example of bifurcation to homoclinic orbits
    • CHOW S. N., HALE J. K. & MALLET-PARET J., An example of bifurcation to homoclinic orbits, J. diff. Eqns 37, 351-373 (1980).
    • (1980) J. Diff. Eqns , vol.37 , pp. 351-373
    • Chow, S.N.1    Hale, J.K.2    Mallet-Paret, J.3
  • 5
    • 48549112859 scopus 로고
    • Exponential dichotomies and transversal homoclinic points
    • PALMER K. J., Exponential dichotomies and transversal homoclinic points, J. diff. Eqns 55, 225-256 (1984).
    • (1984) J. Diff. Eqns , vol.55 , pp. 225-256
    • Palmer, K.J.1
  • 6
    • 0010668206 scopus 로고
    • Perturbing diffeomorphisms which have heteroclinic orbits with semi-hyperbolic fixed points
    • BATTELLI F., Perturbing diffeomorphisms which have heteroclinic orbits with semi-hyperbolic fixed points, Dynam. Sys. Appl. 3, 305-332 (1994).
    • (1994) Dynam. Sys. Appl. , vol.3 , pp. 305-332
    • Battelli, F.1
  • 7
    • 0040862828 scopus 로고
    • Bifurcations of heteroclinic orbits for diffeomorphisms
    • FEČKAN M., Bifurcations of heteroclinic orbits for diffeomorphisms, Appl. Math. 36, 355-367 (1991).
    • (1991) Appl. Math. , vol.36 , pp. 355-367
    • Fečkan, M.1
  • 8
    • 0010746733 scopus 로고
    • On the existence of chaotic behaviour of diffeomorphism
    • FEČKAN M., On the existence of chaotic behaviour of diffeomorphism, Appl. Math. 38, 101-122 (1993).
    • (1993) Appl. Math. , vol.38 , pp. 101-122
    • Fečkan, M.1
  • 9
    • 38249009784 scopus 로고
    • Bounded solutions to singularly perturbed systems of O.D.E
    • BATTELLI F. & LAZZARI C., Bounded solutions to singularly perturbed systems of O.D.E., J. diff. Eqns 100, 49-81 (1992).
    • (1992) J. Diff. Eqns , vol.100 , pp. 49-81
    • Battelli, F.1    Lazzari, C.2
  • 10
    • 0040748657 scopus 로고
    • Melnikov functions for singularly perturbed ordinary differential equations
    • FEČKAN M., Melnikov functions for singularly perturbed ordinary differential equations, Nonlinear Analysis 19, 393-401 (1992).
    • (1992) Nonlinear Analysis , vol.19 , pp. 393-401
    • Fečkan, M.1
  • 11
    • 85030046872 scopus 로고    scopus 로고
    • Chaos in singularly perturbed impulsive O.D.E
    • to appear
    • FEČKAN M., Chaos in singularly perturbed impulsive O.D.E., Boll. Un. mat. Ital. (to appear).
    • Boll. Un. Mat. Ital.
    • Fečkan, M.1
  • 12
    • 0000940089 scopus 로고
    • Chaos in the Duffing equation
    • BATTELLI F. & PALMER K. J., Chaos in the Duffing equation, J. diff. Eqns 101, 276-301 (1993).
    • (1993) J. Diff. Eqns , vol.101 , pp. 276-301
    • Battelli, F.1    Palmer, K.J.2
  • 13
    • 0041800961 scopus 로고
    • Generalized Melnikov functions and existence of bounded solutions in systems with parameters
    • Edited by G. FUSCO, M. IANNELLI and L. SALVADORI, Academic Press, Boston
    • BATTELLI F. & LAZZARI C., Generalized Melnikov functions and existence of bounded solutions in systems with parameters, in Advanced Topics in the Theory of Dynamical Systems (Edited by G. FUSCO, M. IANNELLI and L. SALVADORI), pp. 11-25. Academic Press, Boston (1989).
    • (1989) Advanced Topics in the Theory of Dynamical Systems , pp. 11-25
    • Battelli, F.1    Lazzari, C.2
  • 14
    • 0001261668 scopus 로고
    • Exponential dichotomies, the shadowing lemma and transversal homoclinic points
    • PALMER K. J., Exponential dichotomies, the shadowing lemma and transversal homoclinic points, Dyn. Rep. 1, 265-306 (1988).
    • (1988) Dyn. Rep. , vol.1 , pp. 265-306
    • Palmer, K.J.1
  • 15
    • 26344435066 scopus 로고    scopus 로고
    • Note on a local invertibility
    • to appear
    • FEČKAN M., Note on a local invertibility, Math. Slov. (to appear).
    • Math. Slov.
    • Fečkan, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.