Bob Rink

prof. dr.

20002019
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Research Output 2000 2019

2019

Center manifolds of coupled cell networks

Nijholt, E., Rink, B. & Sanders, J., Mar 2019, In : SIAM Review. 61, 1, p. 121-155 35 p.

Research output: Contribution to JournalReview articleAcademicpeer-review

Center Manifold
Dynamical systems
Cell
Synchrony
Dynamical system

Following periodic orbits through bifurcations

Queirolo, E., 2019, 159 p.

Research output: PhD ThesisPhD Thesis - Research VU, graduation VUAcademic

Open Access
File
2018

Bifurcations in Network Dynamical Systems

Nijholt, E. C., 2018, 220 p.

Research output: PhD ThesisPhD Thesis - Research VU, graduation VUAcademic

Open Access
File

Computer Assisted Proofs in Dynamics and Delay Equations

Groothedde, C. M., 2018, 174 p.

Research output: PhD ThesisPhD Thesis - Research VU, graduation VUAcademic

Open Access
File

Validated Chebyshev-based Computations for Ordinary and Partial Differential Equations

Sheombarsing, R. S. S., 2018, 219 p.

Research output: PhD ThesisPhD Thesis - Research VU, graduation VUAcademic

Open Access
File
2017

Center manifolds of coupled cell networks

Rink, B. W., Nijholt, E. C. & Sanders, J. A., 2017, In : SIAM Journal on Mathematical Analysis. 49, 5, p. 4117-4148

Research output: Contribution to JournalArticleAcademicpeer-review

Center Manifold
Cell
Machinery
Dynamical systems
Vector Field

Projection blocks in homogeneous coupled cell networks

Rink, B. W., Nijholt, E. C. & Sanders, J. A., 2017, In : Dynamical Systems-an International Journal. 32, 1, p. 164-186

Research output: Contribution to JournalArticleAcademicpeer-review

Projection
Cell
Bifurcation
Feedforward Networks
Subset
2016

Graph fibrations and symmetries of network dynamics

Rink, B. W., Sanders, J. A. & Nijholt, E. C., 2016, In : Journal of Differential Equations. 261, p. 4861-4896

Research output: Contribution to JournalArticleAcademicpeer-review

2014

Continuity of the Peierls barrier and robustness of laminations

Mramor, B. & Rink, B. W., 13 Mar 2014, In : Ergodic theory and dynamical systems. 26 p.

Research output: Contribution to JournalArticleAcademicpeer-review

Lamination
Robustness

Coupled cell networks: semigroups, Lie algebras and normal forms

Rink, B. W. & Sanders, J. A., 2014, In : Transactions of the American Mathematical Society. 367, 5, p. 3509-3548 40 p.

Research output: Contribution to JournalArticleAcademicpeer-review

Network architecture
Normal Form
Algebra
Lie Algebra
Semigroup

Coupled cell networks and their hidden symmetries

Rink, B. W. & Sanders, J. A., 2014, In : SIAM Journal on Mathematical Analysis. 46, 2, p. 1577-1609

Research output: Contribution to JournalArticleAcademicpeer-review

Dynamical systems
Symmetry
Cell
Semigroup
Bifurcation

On the destruction of minimal foliations

Mramor, B. & Rink, B. W., 2014, In : Proceedings of the London Mathematical Society. 108, p. 704-737

Research output: Contribution to JournalArticleAcademicpeer-review

Recurrence relation
Foliation
Twist Map
Lamination
Rotation number

The laminations of a crystal near an anti-continuum limit

Knibbeler, V., Mramor, B. & Rink, B. W., 2014, In : Nonlinearity. 27, p. 927-952

Research output: Contribution to JournalArticleAcademicpeer-review

Lamination
Continuum Limit
laminates
Crystal
Twist Map
2013

A dichotomy theorem for minimizers of monotone recurrence relations

Mramor, B. & Rink, B. W., 2013, In : Ergodic theory and dynamical systems. 34 p.

Research output: Contribution to JournalArticleAcademicpeer-review

Global Minimizer
Dichotomy
Recurrence relation
Minimizer
Monotone

Amplified Hopf bifurcations in feed-forward networks

Rink, B. W. & Sanders, J. A., 2013, In : SIAM Journal on Applied Dynamical Systems. 12, 2, p. 1135-1157

Research output: Contribution to JournalArticleAcademicpeer-review

Feedforward Networks
Hopf bifurcation
Hopf Bifurcation
Dynamical systems
Feedforward
2012

Ghost circles in lattice Aubry-Mather theory

Mramor, B. & Rink, B. W., 2012, In : Journal of Differential Equations. 252, 4, p. 3163-3208

Research output: Contribution to JournalArticleAcademicpeer-review

Open Access
Circle
Gradient Flow
Recurrence relation
Hamiltonians
Lattice vibrations

Monotone Variational Recurrence Relations

Mramor, B., 2012

Research output: PhD ThesisPhD Thesis - Research VU, graduation VUAcademic

Open Access
File
2011

Analysis of a model for ship maneuvering

Apri, M., Banagaay, N., van den Berg, G. J. B., Brussee, R., Bourne, D., Fatima, T., Irzal, F., Rademacher, J., Rink, B. W., Veerman, F. & Verpoort, S., 2011, Proceedings of the 79th European study group Mathematics with Industry. Amsterdam, p. 83-116

Research output: Chapter in Book / Report / Conference proceedingConference contributionAcademicpeer-review

2009

Branching patterns of wave trains in the FPU lattice

Guo, S. J., Lamb, J. S. W. & Rink, B. W., 2009, In : Nonlinearity. 22, p. 283-299

Research output: Contribution to JournalArticleAcademicpeer-review

Branching
Hamiltonians
Hamiltonian Structure
Bifurcation
Lyapunov-Schmidt Reduction

Fermi Pasta Ulam systems (FPU): mathematical aspects

Rink, B. W., 2009, In : Scholarpedia Journal. 4, 12, p. 9217-9217

Research output: Contribution to JournalArticleAcademicpeer-review

Open Access
2008

An integrable approximation for the Fermi-Pasta-Ulam lattice

Rink, B. W., 2008, The Fermi-Pasta-Ulam problem. Berlin: Springer, p. 283-301 (Lecture Notes in Phys.; no. 728).

Research output: Chapter in Book / Report / Conference proceedingChapterAcademicpeer-review

2006

Proof of Nishida's conjecture on anharmonic lattices

Rink, B. W., 2006, In : Communications in Mathematical Physics. 261, 3, p. 613-627

Research output: Contribution to JournalArticleAcademicpeer-review

2005

Stability in Hamiltonian systems

Rink, B. W., Tuwankotta, J. M. & Meyer, K. R., 2005, Geometric Mechanics and Symmetry; the Peyresq Lectures'. Montaldi, J. & Ratiu, T. (eds.). Cambridge UP

Research output: Chapter in Book / Report / Conference proceedingChapterAcademicpeer-review

2004

A Cantor set of tori with monodromy near a focus-focus singularity

Rink, B. W., 2004, In : Nonlinearity. 17, p. 347-356

Research output: Contribution to JournalArticleAcademicpeer-review

2003

Symmetric invariant manifolds in the Fermi-Pasta-Ulam lattice

Rink, B. W., 2003, In : Physica D. Nonlinear Phenomena. 175, p. 31-42

Research output: Contribution to JournalArticleAcademicpeer-review

2002

Direction reversing traveling waves in the even Fermi-Pasta-Ulam lattice

Rink, B. W., 2002, In : Journal of nonlinear science. 12, p. 479-504

Research output: Contribution to JournalArticleAcademicpeer-review

Traveling waves and monodromy in anharmonic lattices

Rink, B. W., 2002, Proceedings of the international conference SPT2002. Abenda, S. (ed.). World Scientific, p. 217-220

Research output: Chapter in Book / Report / Conference proceedingChapterAcademicpeer-review

2001

A symmetric normal form for the Fermi Pasta Ulam chain

Rink, B. W., 2001, Proceedings of the international conference SPT2001. Bambusi, D. (ed.). World Scientific

Research output: Chapter in Book / Report / Conference proceedingConference contributionAcademicpeer-review

Symmetry and resonance in periodic FPU chains

Rink, B. W., 2001, In : Communications in Mathematical Physics. 218, p. 665-685

Research output: Contribution to JournalArticleAcademicpeer-review

2000

Near-integrability of periodic FPU-chains

Rink, B. W. & Verhulst, F., 2000, In : Physica A. Statistical Mechanics and its Applications. 285, p. 467-482

Research output: Contribution to JournalArticleAcademicpeer-review