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Lattice structures for attractors I
1. | Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, 33431 Boca Raton |
2. | Rutgers University, 110 Frelinghusen Road, Piscataway, NJ 08854 |
3. | VU University, De Boelelaan 1081a, 1081 HV, Amsterdam, Netherlands |
References:
[1] |
E. Akin, The General Topology of Dynamical Systems, vol. 1 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 1993. |
[2] |
Z. Arai, W. D. Kalies, H. Kokubu, K. Mischaikow, H. Oka and P. Pilarczyk, A database schema for the analysis of global dynamics of multiparameter systems, SIAM J. Appl. Dyn. Syst., 8 (2009), 757-789.
doi: 10.1137/080734935. |
[3] |
K. A. Baker and A. W. Hales, Distributive projective lattices, Canad. J. Math., 22 (1970), 472-475.
doi: 10.4153/CJM-1970-054-0. |
[4] |
H. Ban and W. D. Kalies, A computational approach to Conley's decomposition theorem, J. Comp. Nonlinear Dynamics, 1 (2006), 312-319.
doi: 10.1115/1.2338651. |
[5] |
J. Bush, M. Gameiro, S. Harker, H. Kokubu, K. Mischaikow, I. Obayashi and P. Pilarczyk, Combinatorial-topological framework for the analysis of global dynamics, CHAOS, 22 (2012), 047508.
doi: 10.1063/1.4767672. |
[6] |
C. Conley, Isolated Invariant Sets and the Morse Index, vol. 38 of CBMS Regional Conference Series in Mathematics, American Mathematical Society, Providence, R.I., 1978. |
[7] |
B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, 2nd edition, Cambridge University Press, New York, 2002.
doi: 10.1017/CBO9780511809088. |
[8] |
R. Franzosa, Index filtrations and the homology index braid for partially ordered Morse decompositions, Trans. Amer. Math. Soc., 298 (1986), 193-213.
doi: 10.1090/S0002-9947-1986-0857439-7. |
[9] |
R. D. Franzosa and K. Mischaikow, The connection matrix theory for semiflows on (not necessarily locally compact) metric spaces, J. Differential Equations, 71 (1988), 270-287.
doi: 10.1016/0022-0396(88)90028-9. |
[10] |
R. Freese and J. B. Nation, Projective lattices, Pacific J. Math., 75 (1978), 93-106, URL http://projecteuclid.org/euclid.pjm/1102810149.
doi: 10.2140/pjm.1978.75.93. |
[11] |
G. Grätzer, Lattice Theory: Foundation, Birkhäuser/Springer Basel AG, Basel, 2011.
doi: 10.1007/978-3-0348-0018-1. |
[12] |
W. Kalies, K. Mischaikow and R. C. Vandervorst, An algorithmic approach to chain recurrence, Found. Comput. Math., 5 (2005), 409-449.
doi: 10.1007/s10208-004-0163-9. |
[13] |
W. Kalies, K. Mischaikow and R. C. Vandervorst, Lattice structures for attractors II, Submitted for publication, arXiv:1409.5405. |
[14] |
E. Liz and P. Pilarczyk, Global dynamics in a stage-structured discrete-time population model with harvesting, J. Theoret. Biol., 297 (2012), 148-165.
doi: 10.1016/j.jtbi.2011.12.012. |
[15] |
F. Miraglia, An Introduction to Partially Ordered Structures and Sheaves, vol. 1 of Contemporary Logic Series, Polimetrica Scientific Publisher, Milan, Italy, 2006. |
[16] |
J. W. Robbin and D. A. Salamon, Lyapunov maps, simplicial complexes and the Stone functor, Ergodic Theory Dynam. Systems, 12 (1992), 153-183.
doi: 10.1017/S0143385700006647. |
[17] |
C. Robinson, Dynamical Systems, 2nd edition, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1999, Stability, Symbolic dynamics, and Chaos. |
[18] |
S. Roman, Lattices and Ordered Sets, Springer, New York, 2008. |
[19] |
S. Vickers, Topology via Logic, vol. 5 of Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, Cambridge, 1989. |
show all references
References:
[1] |
E. Akin, The General Topology of Dynamical Systems, vol. 1 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 1993. |
[2] |
Z. Arai, W. D. Kalies, H. Kokubu, K. Mischaikow, H. Oka and P. Pilarczyk, A database schema for the analysis of global dynamics of multiparameter systems, SIAM J. Appl. Dyn. Syst., 8 (2009), 757-789.
doi: 10.1137/080734935. |
[3] |
K. A. Baker and A. W. Hales, Distributive projective lattices, Canad. J. Math., 22 (1970), 472-475.
doi: 10.4153/CJM-1970-054-0. |
[4] |
H. Ban and W. D. Kalies, A computational approach to Conley's decomposition theorem, J. Comp. Nonlinear Dynamics, 1 (2006), 312-319.
doi: 10.1115/1.2338651. |
[5] |
J. Bush, M. Gameiro, S. Harker, H. Kokubu, K. Mischaikow, I. Obayashi and P. Pilarczyk, Combinatorial-topological framework for the analysis of global dynamics, CHAOS, 22 (2012), 047508.
doi: 10.1063/1.4767672. |
[6] |
C. Conley, Isolated Invariant Sets and the Morse Index, vol. 38 of CBMS Regional Conference Series in Mathematics, American Mathematical Society, Providence, R.I., 1978. |
[7] |
B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, 2nd edition, Cambridge University Press, New York, 2002.
doi: 10.1017/CBO9780511809088. |
[8] |
R. Franzosa, Index filtrations and the homology index braid for partially ordered Morse decompositions, Trans. Amer. Math. Soc., 298 (1986), 193-213.
doi: 10.1090/S0002-9947-1986-0857439-7. |
[9] |
R. D. Franzosa and K. Mischaikow, The connection matrix theory for semiflows on (not necessarily locally compact) metric spaces, J. Differential Equations, 71 (1988), 270-287.
doi: 10.1016/0022-0396(88)90028-9. |
[10] |
R. Freese and J. B. Nation, Projective lattices, Pacific J. Math., 75 (1978), 93-106, URL http://projecteuclid.org/euclid.pjm/1102810149.
doi: 10.2140/pjm.1978.75.93. |
[11] |
G. Grätzer, Lattice Theory: Foundation, Birkhäuser/Springer Basel AG, Basel, 2011.
doi: 10.1007/978-3-0348-0018-1. |
[12] |
W. Kalies, K. Mischaikow and R. C. Vandervorst, An algorithmic approach to chain recurrence, Found. Comput. Math., 5 (2005), 409-449.
doi: 10.1007/s10208-004-0163-9. |
[13] |
W. Kalies, K. Mischaikow and R. C. Vandervorst, Lattice structures for attractors II, Submitted for publication, arXiv:1409.5405. |
[14] |
E. Liz and P. Pilarczyk, Global dynamics in a stage-structured discrete-time population model with harvesting, J. Theoret. Biol., 297 (2012), 148-165.
doi: 10.1016/j.jtbi.2011.12.012. |
[15] |
F. Miraglia, An Introduction to Partially Ordered Structures and Sheaves, vol. 1 of Contemporary Logic Series, Polimetrica Scientific Publisher, Milan, Italy, 2006. |
[16] |
J. W. Robbin and D. A. Salamon, Lyapunov maps, simplicial complexes and the Stone functor, Ergodic Theory Dynam. Systems, 12 (1992), 153-183.
doi: 10.1017/S0143385700006647. |
[17] |
C. Robinson, Dynamical Systems, 2nd edition, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1999, Stability, Symbolic dynamics, and Chaos. |
[18] |
S. Roman, Lattices and Ordered Sets, Springer, New York, 2008. |
[19] |
S. Vickers, Topology via Logic, vol. 5 of Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, Cambridge, 1989. |
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