Paul Glendinning
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British mathematician
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Mathematics
Paul Glendinning's Degrees
- PhD Mathematics University of Manchester
- Bachelors Mathematics University of Manchester
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Why Is Paul Glendinning Influential?
(Suggest an Edit or Addition)According to Wikipedia, Paul Glendinning is a professor of Applied Mathematics, in the School of Mathematics at the University of Manchester who is known for his work on dynamical systems, specifically models of the time-evolution of complex mathematical or physical processes. His main areas of research are bifurcation theory ; synchronization and blowout bifurcations; low-dimensional mapss; and quasi-periodically forced systems.
Paul Glendinning's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations (1994) (592)
- Local and global behavior near homoclinic orbits (1984) (410)
- From finite to infinite dimensional dynamical systems (2001) (396)
- UNIQUE REPRESENTATIONS OF REAL NUMBERS IN NON-INTEGER BASES (2001) (163)
- T-points: A codimension two heteroclinic bifurcation (1986) (123)
- Key questions for modelling COVID-19 exit strategies (2020) (98)
- The mathematics of motion camouflage (2004) (95)
- Melnikov analysis of chaos in a simple epidemiological model (1997) (72)
- Global structure of periodicity hubs in Lyapunov phase diagrams of dissipative flows. (2011) (69)
- The Princeton companion to applied mathematics (2015) (63)
- Prime and renormalisable kneading invariants and the dynamics of expanding Lorenz maps (1993) (60)
- Bifurcations near homoclinic orbits with symmetry (1984) (59)
- Topological conjugation of Lorenz maps by β-transformations (1990) (57)
- Modelling human balance using switched systems with linear feedback control (2012) (54)
- The gluing bifurcation: I. Symbolic dynamics of closed curves (1988) (48)
- Zeros of the kneading invariant and topological entropy for Lorenz maps (1996) (44)
- Multistability and nonsmooth bifurcations in the Quasiperiodically forced Circle Map (2000) (40)
- Global attractors of pinched skew products (2002) (39)
- Rotation numbers for quasi-periodically forced monotone circle maps (2002) (30)
- How chaotic are strange non-chaotic attractors? (2006) (29)
- Locating bifurcations in quasiperiodically forced systems (1995) (26)
- Imperfect homoclinic bifurcations. (2001) (25)
- Collage de cycles et suites de Farey (1984) (24)
- Oscillatory bubbles induced by geometrical constraint (2011) (24)
- The doubling map with asymmetrical holes (2013) (24)
- Grazing-sliding bifurcations, border collision maps and the curse of dimensionality for piecewise smooth bifurcation theory (2014) (24)
- Robust chaos revisited (2017) (22)
- Bifurcation from stable fixed point to N-dimensional attractor in the border collision normal form (2015) (22)
- Mechanisms of Intermittent State Transitions in a Coupled Heterogeneous Oscillator Model of Epilepsy (2013) (22)
- The structure of mode-locked regions in quasi-periodically forced circle maps (2000) (22)
- Milnor attractors and topological attractors of a piecewise linear map (2001) (22)
- Stability, Instability and Chaos: Index (1994) (21)
- Two-dimensional attractors in the border-collision normal form (2011) (21)
- Stability, Instability and Chaos: CHAOS (1994) (20)
- Bifurcation from stable fixed point to 2D attractor in the border collision normal form (2016) (20)
- Stable Cycles with Complicated Structure (1985) (20)
- Transitivity and blowout bifurcations in a class of globally coupled maps (1999) (19)
- New Directions in Dynamical Systems: Global Bifurcations in Flows (1988) (18)
- Boundary-equilibrium bifurcations in piecewise-smooth slow-fast systems. (2011) (18)
- Classification of boundary equilibrium bifurcations in planar Filippov systems. (2016) (18)
- Attractors near grazing–sliding bifurcations (2012) (18)
- An Introduction to Piecewise Smooth Dynamics (2019) (18)
- The stability boundary of synchronized states in globally coupled dynamical systems (1999) (17)
- Shilnikov chaos, Filippov sliding and boundary equilibrium bifurcations (2018) (17)
- TRAVELLING WAVES WITH SPATIALLY RESONANT FORCING: BIFURCATIONS OF A MODIFIED LANDAU EQUATION (1993) (16)
- Non-smooth pitchfork bifurcations (2004) (16)
- The Border Collision Normal Form with Stochastic Switching Surface (2014) (15)
- Bifocal homoclinic bifurcations (1997) (15)
- Nonparametric Estimation for Financial Investment under Log-Utility (2007) (15)
- Heteroclinic loops leading to hyperchaos (1985) (14)
- Stability, Instability and Chaos: GLOBAL BIFURCATION THEORY (1994) (14)
- The anharmonic route to chaos: kneading theory (1993) (14)
- Multiple attractors in grazing–sliding bifurcations in Filippov-type flows (2016) (13)
- Intermittency and strange nonchaotic attractors in quasi-periodically forced circle maps (1998) (13)
- Subsidiary bifurcations near bifocal homoclinic orbits (1989) (13)
- Border collision bifurcations, snap-back repellers, and chaos. (2009) (13)
- Micro-chaotic dynamics due to digital sampling in hybrid systems of Filippov type (2010) (13)
- A constructive approach to robust chaos using invariant manifolds and expanding cones (2021) (13)
- The rotation interval as a computable measure of chaos (1984) (12)
- Bifurcations of SNAP-Back Repellers with Application to Border-Collision bifurcations (2010) (12)
- Robust new routes to chaos in differential equations (1992) (12)
- Differential Equations with Bifocal Homoclinic Orbits (1997) (11)
- Explicit renormalisation in piecewise linear bimodal maps (1990) (11)
- The nonsmooth pitchfork bifurcation (2004) (11)
- Grazing-sliding bifurcations, the border collision normal form, and the curse of dimensionality for nonsmooth bifurcation theory (2012) (11)
- Renormalisation between classes of maps (1990) (11)
- Lyapunov exponent and topological entropy plateaus in piecewise linear maps (2013) (11)
- Chaos in Dynamical Systems., by E. Ott (1994) (11)
- Non-smooth Hopf-type bifurcations arising from impact–friction contact events in rotating machinery (2014) (11)
- D S ] 1 3 A pr 2 00 6 How chaotic are strange nonchaotic attractors ? (2014) (10)
- Geometry of Refractions and Reflections Through a Biperiodic Medium (2016) (9)
- Fine structure of mode-locked regions of the quasi-periodically forced circle map (1999) (9)
- Travelling wave solutions near isolated double-pulse solitary waves of nerve axon equations (1987) (9)
- Global structure of homoclinic bifurcations: a combinatorial approach (1989) (9)
- Two-ball Newton's cradle. (2011) (8)
- Hyperbolicity of the invariant set for the logistic map with μ>4☆ (2001) (8)
- Towards a quasi-periodic mean field theory for globally coupled oscillators (1999) (8)
- Emergence of hierarchical networks and polysynchronous behaviour in simple adaptive systems (2011) (8)
- A dynamic, spatially periodic, micro‐pattern of HES5 underlies neurogenesis in the mouse spinal cord (2021) (7)
- SHILNIKOV’S SADDLE-NODE BIFURCATION (1996) (7)
- Robust chaos and the continuity of attractors (2019) (7)
- Strangely dispersed minimal sets in the quasiperiodically forced Arnold circle map (2008) (7)
- Potential solutions to voltage control issues for distribution networks containing independent generators (2001) (7)
- Less is More I: a pessimistic view of piecewise smooth bifurcation theory (2017) (6)
- Renormalization for the boundary of chaos in piecewise monotonic maps with a single discontinuity (2014) (6)
- Bifurcations And Rotation Numbers for Maps of The Circle Associated With Flows on The Torus And Models of Cardiac Arrhythmias (1995) (6)
- Asymmetric perturbations of Lorenz-like equations (1987) (5)
- Stability, Instability and Chaos: STABILITY (1994) (5)
- Island chain models and gradient systems (1994) (5)
- Visual and vestibular determinants of the translational vestibulo‐ocular reflex (2011) (5)
- Auto-regressive moving average analysis of linear and discontinuous models of human balance during quiet standing. (2014) (4)
- Hierarchy and polysynchrony in an adaptive network. (2014) (4)
- A dynamic, spatially periodic, micro-pattern of HES5 underlies neurogenesis in the mouse spinal cord (2020) (4)
- Stability, Instability and Chaos: INTRODUCTION (1994) (4)
- Invariant measures of the border collision normal form (2011) (4)
- Homoclinic Bifurcations in Ordinary Differential Equations (1987) (4)
- Adaptive resonance and pumping a swing (2020) (4)
- Invariant Measures for the n-Dimensional Border Collision Normal Form (2014) (4)
- VIEW FROM THE PENNINES: NON-TRIVIAL PURSUITS (2003) (3)
- State transitions in a model of intermittent seizure dynamics (2012) (3)
- Creation of discontinuities in circle maps (2019) (3)
- VIEW FROM THE PENNINES: MAKING CONNECTIONS (2003) (3)
- Constructing robust chaos: invariant manifolds and expanding cones (2019) (3)
- Chaos in the border-collision normal form: A computer-assisted proof using induced maps and invariant expanding cones (2021) (3)
- Routes to Chaos (2005) (2)
- SHAKING AND WHIRLING: DYNAMICS OF SPIDERS AND THEIR WEBS (2018) (2)
- THE NON-SMOOTH PITCHFORK BIFURCATION (2002) (2)
- Lacunarity and period-doubling (2013) (2)
- Inaccessible attractors of weakly dissipative systems (1997) (2)
- Stability, Instability and Chaos: LINEAR DIFFERENTIAL EQUATIONS (1994) (2)
- Inclusion of higher-order terms in the border-collision normal form: persistence of chaos and applications to power converters (2021) (2)
- Regularization by External Variables (2017) (2)
- VIEW FROM THE PENNINES: ANALYSIS ON TIME SCALES (2003) (2)
- Multiple attractors in grazing-sliding bifurcations in an explicit example of a Filippov type flow (2011) (2)
- Multistability in the quasiperiodically forced circle map (2001) (2)
- Smooth conjugacy of difference equations derived from elliptic curves (2021) (2)
- Dynamic switching of lateral inhibition spatial patterns (2022) (1)
- STABILITY OF ASYMMETRIC CLUSTER STATES IN GLOBALLY COUPLED MAPS (2003) (1)
- TWO DIMENSIONAL DYNAMICS (1994) (1)
- Dynamics of a hybrid thermostat model with discrete sampling time control (2009) (1)
- Micro-chaos in Relay Feedback Systems with Bang-Bang Control and Digital Sampling (2011) (1)
- Hidden dynamics for piecewise smooth maps (2021) (1)
- Controland Coordination in Human Balance Influence of Stance Width on Frontal Plane Postural (2015) (1)
- Families of piecewise linear maps with constant Lyapunov exponent (2012) (1)
- Universal scaling of rotation intervals for quasi-periodically forced circle maps (2012) (1)
- Normal Forms, Differentiable Conjugacies, and Elementary Bifurcations of Maps (2022) (1)
- VIEW FROM THE PENNINES: STRANGE NONCHAOTIC ATTRACTORS (2008) (1)
- Piecewise-smooth Flows (2019) (1)
- Pausing for arbitrarily long times in dynamical systems (2019) (1)
- Normal forms for saddle-node bifurcations: Takens’ coefficient and applications in climate models (2022) (1)
- VIEW FROM THE PENNINES: BEYOND MAL-RULES (2008) (1)
- VIEW FROM THE PENNINES: BOX MODELS OF THE OCEANIC CONVEYOR BELT (2009) (1)
- Math in minutes (2013) (1)
- Perspectives of Nonlinear Dynamics. By E. ATLEE JACKSON. Cambridge University Press, 1991. Vol. 1, 469 pp., £19.95; vol. 2, 633 pp., £19.95. (1993) (1)
- Stability, Instability and Chaos: PERTURBATION THEORY (1994) (0)
- Invariant manifolds and sets (2005) (0)
- Stability, Instability and Chaos: Notation (1994) (0)
- Part I. Introduction to Applied Mathematics (2015) (0)
- Dynamics of planar piecewise-smooth slow-fast systems (2010) (0)
- Stability, Instability and Chaos: BIFURCATIONAL MISCELLANY (1994) (0)
- VIEW FROM THE PENNINES: ABSTRACT FROST FRONTS (2010) (0)
- Time Series Near Codimension Two Global Bifurcations (1989) (0)
- Stability, Instability and Chaos: LINEARIZATION AND HYPERBOLICITY (1994) (0)
- VIEW FROM THE PENNINES: ON ART AND CAUSAL SETS (2004) (0)
- VIEW FROM THE PENNINES: MONTESSORI MATHEMATICS (2005) (0)
- The Two Ball Newton ’ s Cradle Glendinning , Paul 2011 (2017) (0)
- Characterizing Tipping in a Stochastic Reduced Stommel-Type Model in Higher-Dimensions (2017) (0)
- VIEW FROM THE PENNINES: USING MATHS I, TOMOGRAPHY AND FRITZ JOHN (2006) (0)
- Stability, Instability and Chaos: Bibliography (1994) (0)
- Part III. Equations, Laws, and Functions of Applied Mathematics (2015) (0)
- VIEW FROM THE PENNINES : TEN MARTINIS AND FRACTAL CARPETS (2005) (0)
- VIEW FROM THE PENNINES: STICKY WAVES (2003) (0)
- Maths in Minutes: 200 Key Concepts Explained in an Instant (2012) (0)
- A physicist's tour of chaos (1994) (0)
- Mechanisms of Intermittent State Transitions in a Coupled Heterogeneous Oscillator Model of Epilepsy (2013) (0)
- Wind farms : connecting to the UK electricity grid (2006) (0)
- Notes and further reading (1994) (0)
- Transition from stable orbit to chaotic dynamics in hybrid systems of Filippov type with digital sampling (2009) (0)
- Differentiable conjugacies for one-dimensional maps (2023) (0)
- Heterodimensional cycles and noninvertible blenders in piecewise smooth two dimensional maps (2023) (0)
- FROM THE PENNINES : WHAT HAS MATHEMATICS DONE FOR US ? (2006) (0)
- Introduction to the dynamics of piecewise smooth maps (2016) (0)
- VIEW FROM THE PENNINES: EULER GOES BALLISTIC (2007) (0)
- The accumulation of boundary doubling for modified tent maps (2003) (0)
- VIEW FROM THE PENNINES: EULER GETS KINKY (2007) (0)
- Part VIII. Final Perspectives (2015) (0)
- Bifurcation from stable fixed point to two-dimensional attractor in the border collision normal form Glendinning (2017) (0)
- Piecewise-smooth Maps (2019) (0)
- VIEW FROM THE PENNINES: NEWTONIAN CHOREOGRAPHIES (2002) (0)
- Unstable dimension variability, heterodimensional cycles, and blenders in the border-collision normal form (2022) (0)
- VIEW FROM THE PENNINES: A COSMIC INDIAN ROPE TRICK (2010) (0)
- FROM THE PENNINES : CARLESON , STRANGE ATTRACTORS AND THE ABEL PRIZE 2006 (2006) (0)
- BIFURCATION THEORY II: PERIODIC ORBITS AND MAPS (1994) (0)
- FROM THE PENNINES : ANALYSIS ON TIME SCALES (2003) (0)
- Part VI. Example Problems (2015) (0)
- Maths in Minutes (2013) (0)
- Part VII. Application Areas (2015) (0)
- Part V. Modeling (2015) (0)
- VIEW FROM THE PENNINES: IDEAL KNOTS (2003) (0)
- VIEW FROM THE PENNINES: SYSTEMS BIOLOGY (2005) (0)
- VIEW FROM THE PENNINES: PREFERENCE AND UTILITY (2004) (0)
- Stability, Instability and Chaos: BIFURCATION THEORY I: STATIONARY POINTS (1994) (0)
- Robust chaos revisited (2017) (0)
- Stability, Instability and Chaos: Preface (1994) (0)
- Uncountably Many Cases of Filippov’s Sewed Focus (2023) (0)
- FROM THE PENNINES : PATTERN COMPLEXITY (2004) (0)
- A dynamic and spatially periodic micro-pattern of HES5 expression underlies the probability of neuronal differentiation in the mouse spinal cord (2020) (0)
- Part II. Concepts (2015) (0)
- FROM THE PENNINES : MIND THE ( GENERATION ) GAP (2010) (0)
- Part IV. Areas of Applied Mathematics (2015) (0)
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