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 and 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 and 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 and 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 and 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 and 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 and 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 and 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 and 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 and 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 and 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 and 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 and 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 and 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 and 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 and 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 and 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 and 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 and 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 and 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 (65)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy