American Institute of Mathematical Sciences

Advanced
August  2007, 17(3): 653-670. doi: 10.3934/dcds.2007.17.653

Structure of index sequences for mappings with an asymptotic derivative

Alexei Pokrovskii 1, and  Oleg Rasskazov 1,

1. 

Department of Applied Mathematics, University College, Cork, Ireland, Ireland

Received  February 2006 Revised  July 2006 Published  December 2006

Properties of the sequence ind$(\infty,\id-f^{m}),$ $m=1,2,\ldots$ where $f^{m}$ is the $m$-th iterate of the mapping $ f:R^{d}\to R^{d}$, and ind denotes the Kronecker index are investigated. The case when $f$ has the asymptotic derivative $A$ at infinity and some eigenvalues of $A$ are roots of unity is of primary interest.
Keywords: Index sequence, topological degree, index at infinity..
Mathematics Subject Classification: Primary: 58F14; Secondary 58F2.
Citation: Alexei Pokrovskii, Oleg Rasskazov. Structure of index sequences for mappings with an asymptotic derivative. Discrete & Continuous Dynamical Systems, 2007, 17 (3) : 653-670. doi: 10.3934/dcds.2007.17.653
[1]

Alexander Krasnosel'skii, Jean Mawhin. The index at infinity for some vector fields with oscillating nonlinearities. Discrete & Continuous Dynamical Systems, 2000, 6 (1) : 165-174. doi: 10.3934/dcds.2000.6.165
[2]

A.M. Krasnosel'skii, Jean Mawhin. The index at infinity of some twice degenerate compact vector fields. Discrete & Continuous Dynamical Systems, 1995, 1 (2) : 207-216. doi: 10.3934/dcds.1995.1.207
[3]

Anna Go??biewska, S?awomir Rybicki. Equivariant Conley index versus degree for equivariant gradient maps. Discrete & Continuous Dynamical Systems - S, 2013, 6 (4) : 985-997. doi: 10.3934/dcdss.2013.6.985
[4]

Luis Barreira, Claudia Valls. Topological conjugacies and behavior at infinity. Communications on Pure & Applied Analysis, 2014, 13 (2) : 687-701. doi: 10.3934/cpaa.2014.13.687
[5]

Litismita Jena, Sabyasachi Pani. Index-range monotonicity and index-proper splittings of matrices. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 379-388. doi: 10.3934/naco.2013.3.379
[6]

Daoyin He, Ingo Witt, Huicheng Yin. On the strauss index of semilinear tricomi equation. Communications on Pure & Applied Analysis, 2020, 19 (10) : 4817-4838. doi: 10.3934/cpaa.2020213
[7]

Elisa Gorla, Maike Massierer. Index calculus in the trace zero variety. Advances in Mathematics of Communications, 2015, 9 (4) : 515-539. doi: 10.3934/amc.2015.9.515
[8]

Ha Pham, Plamen Stefanov. Weyl asymptotics of the transmission eigenvalues for a constant index of refraction. Inverse Problems & Imaging, 2014, 8 (3) : 795-810. doi: 10.3934/ipi.2014.8.795
[9]

Chinmay Kumar Giri. Index-proper nonnegative splittings of matrices. Numerical Algebra, Control & Optimization, 2016, 6 (2) : 103-113. doi: 10.3934/naco.2016002
[10]

Chao Zhang, Jingjing Wang, Naihua Xiu. Robust and sparse portfolio model for index tracking. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1001-1015. doi: 10.3934/jimo.2018082
[11]

Dawei Yang, Shaobo Gan, Lan Wen. Minimal non-hyperbolicity and index-completeness. Discrete & Continuous Dynamical Systems, 2009, 25 (4) : 1349-1366. doi: 10.3934/dcds.2009.25.1349
[12]

Rafael Ortega. Stability and index of periodic solutions of a nonlinear telegraph equation. Communications on Pure & Applied Analysis, 2005, 4 (4) : 823-837. doi: 10.3934/cpaa.2005.4.823
[13]

Todd Young. A result in global bifurcation theory using the Conley index. Discrete & Continuous Dynamical Systems, 1996, 2 (3) : 387-396. doi: 10.3934/dcds.1996.2.387
[14]

Radoslaw Pytlak. Numerical procedure for optimal control of higher index DAEs. Discrete & Continuous Dynamical Systems, 2011, 29 (2) : 647-670. doi: 10.3934/dcds.2011.29.647
[15]

M. C. Carbinatto, K. Mischaikow. Horseshoes and the Conley index spectrum - II: the theorem is sharp. Discrete & Continuous Dynamical Systems, 1999, 5 (3) : 599-616. doi: 10.3934/dcds.1999.5.599
[16]

Stephen Campbell, Peter Kunkel. Solving higher index DAE optimal control problems. Numerical Algebra, Control & Optimization, 2016, 6 (4) : 447-472. doi: 10.3934/naco.2016020
[17]

Yingjie Li, Xiaoguang Yang, Shushang Zhu, Dong-Hui Li. A hybrid approach for index tracking with practical constraints. Journal of Industrial & Management Optimization, 2014, 10 (3) : 905-927. doi: 10.3934/jimo.2014.10.905
[18]

Shirin Panahi, Sajad Jafari. New synchronization index of non-identical networks. Discrete & Continuous Dynamical Systems - S, 2021, 14 (4) : 1359-1373. doi: 10.3934/dcdss.2020371
[19]

Lee Patrolia. Quantitative photoacoustic tomography with variable index of refraction. Inverse Problems & Imaging, 2013, 7 (1) : 253-265. doi: 10.3934/ipi.2013.7.253
[20]

Marius Mitrea. On Bojarski's index formula for nonsmooth interfaces. Electronic Research Announcements, 1999, 5: 40-46.

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (50)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences