Extremal metrics studied with new bifurcation technique.
problem Deformation of extremal metrics.
method Generalized bifurcation technique of Bando-Mabuchi.
result New understanding of extremal metrics through deformation.
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48 results for “bifurcation technique”
The paper studies bifurcations in discrete dynamical systems on manifolds.
problem Understanding bifurcations in discrete dynamical systems on manifolds.
method Topological techniques based on concentricity of manifolds.
result General result for attractors in n-dimensional manifolds.
Study on bifurcations in Lagrangian systems and geodesics on manifolds.
problem Investigating bifurcations in Lagrangian systems and geodesics on Finsler and Riemannian manifolds.
method Employing Morse index and nullity techniques, and refining the Gauss lemma.
result Derivation of precise conditions for bifurcations in geodesic flows.
The paper studies bifurcations in Lagrangian systems and geodesics.
problem Investigating bifurcations in Lagrangian systems with various boundary conditions.
method Using Morse theory and nullity techniques, the paper establishes conditions for bifurcation in three configurations.
result Unified Morse-theoretic framework connecting geometric focal structure and analytic bifurcation behavior.
Study finds multiple periodic solutions to ODEs related to curvature problems.
problem Finding multiple positive periodic solutions to quasilinear ODEs.
method Global bifurcation techniques applied to second order quasilinear ODEs.
result Bifurcation-theoretic proof of nonuniqueness for conformal metrics with constant scalar curvature.
Study finds many nonplanar minimal spheres in elongated ellipsoids.
problem Existence of nonplanar minimal spheres in elongated ellipsoids.
method Global bifurcation techniques to establish existence and quantify number.
result Arbitrarily many nonplanar minimal spheres exist in elongated ellipsoids.
Study degenerate solutions on product of spheres using bifurcation theory.
problem Existence of degenerate solutions on product of spheres.
method Bifurcation theory, isoparametric functions, Gegenbauer polynomials.
result Existence of degenerate solutions that depend on both factors.
New contractible domains on half-sphere with constant boundary Laplacian eigenfunctions.
problem Existence of contractible domains with specific boundary conditions.
method Local bifurcation argument around geodesic disks, anisotropic Hölder spaces, computer-assisted techniques.
result Existence of nontrivial contractible domains on half-sphere with constant boundary Laplacian eigenfunctions.
We study existence and non-existence of constant scalar curvature metrics conformal and arbitrarily close to homogeneous metrics on spheres, using variational techniques. This describes all critical points of the Hilbert-Einstein functional on such conformal classes, near homogeneous metrics. Both bifurcation and local…
Toral CW complexes and bifurcation control in Eulerian flows with multiple Hopf singularitiesmath.DS
Study controls bifurcations in Eulerian flows with multiple Hopf singularities.
problem Bifurcation analysis and control of nonlinear Eulerian flows with non-resonant n-tuple Hopf singularities.
method Analysis of CW complex bifurcations of flow-invariant Clifford hypertori, using leaf-bifurcation varieties.
result Tertiary toral CW complex bifurcates from and persists outside a secondary toral CW complex.
Study bifurcation in Riemannian metrics and submersions.
problem Analyzing bifurcation points in Riemannian metrics.
method Examining a one-parameter family of metrics on total spaces of harmonic Riemannian submersions.
result Existence and characterization of bifurcation points, and sufficient conditions for bifurcation.
Study how invariants change under bifurcations of curves.
problem Understanding how invariants of curves change under bifurcations.
method Analyzing , , , and invariants of curves under -bifurcations.
result Invariant changes under bifurcations, preserving its essential properties.
Projection of crosscapmath.DG
Study bifurcation diagrams of crosscap contours.
problem Understanding bifurcations in crosscap images.
method Determined precise bifurcation diagrams of crosscap contours.
result Three types of equivalences are crucial for bifurcations.
The paper explores mechanisms of market regime transition via slow and fast bifurcations.
problem Understanding and predicting market regime transitions.
method Analyzes slow and fast bifurcations in market dynamics using a Markovian chain diffusion.
result Efficiency of precursors in predicting market regime transitions.
MATLAB toolbox pde2path solves geometric PDEs and finds bifurcations in immersed surfaces.
problem Finding bifurcations in geometric PDEs of immersed surfaces.
method Solving PDEs for surface displacement, updating surface, detecting and localizing bifurcations, and switching branches.
result Symmetry breaking bifurcations in various geometric surfaces.
Study finds bifurcation and local rigidity points for solutions to the Yamabe problem on Aloff-Wallach Spaces.
problem Yamabe problem on Aloff-Wallach Spaces
method Constructing 1-parameter families of solutions and examining changes in the Morse index as the parameter varies.
result Identifies bifurcation and local rigidity points for homogeneous solutions to the Yamabe problem.
Machine learning detects tipping points in complex systems.
problem Detecting abrupt shifts in complex dynamical systems.
method Equilibrium-informed neural networks (EINNs) trained on candidate equilibrium states.
result EINNs can identify critical thresholds in nonlinear systems.
Let (ρ_λ)_{λ\in Λ} be a holomorphic family of representations of a finitely generated group G into PSL(2,C), parameterized by a complex manifold Λ. We define a notion of bifurcation current in this context, that is, a positive closed current on Λdescribing the bifurcations of this family of representations in a quantit…
Study finds multiple solutions for constant scalar curvature on warped products.
problem Finding multiple constant scalar curvature metrics on warped products.
method Bifurcation theory and spectral theory for warped products.
result Proves multiplicity results for the Yamabe problem.
Study bifurcations and local rigidity on flag manifolds for Yamabe solutions.
problem Yamabe problem on maximal flag manifolds
method Determine bifurcation and local rigidity points for 1-parameter families of solutions
result Identify specific points of bifurcation and local rigidity
Study the geometry of bifurcation sets for specific types of functions.
problem Understanding the structure of bifurcation sets for specific types of functions.
method Using blow-ups and parametrization, investigate the Gaussian curvature, principal curvatures, and curve behavior.
result Bifurcation sets of -functions can be parametrized as surfaces in .
Study bifurcation in plane-to-plane germs with specific properties.
problem Understanding the structure of bifurcations in a specific class of geometric objects.
method Explicit description of the bifurcation diagram of the topologically A-versal unfolding.
result Explicit description of the bifurcation diagram for a specific class of plane-to-plane germs.
We consider the Dirichlet problem for semilinear elliptic equations on a bounded domain which is diffeomorphic to a ball and investigate bifurcation from a given (trivial) branch of solutions, where the radius of the ball serves as bifurcation parameter. Our methods are based on well known results from variational bifu…
Example shows not all conjugate points are bifurcation points in semi-Riemannian geodesics.
problem Determining which conjugate points in semi-Riemannian geodesics are bifurcation points.
method Revisiting and correcting an example by Musso, Pejsachowicz, and Portaluri.
result Every conjugate point on the improved example is a bifurcation point.
Ellipsoids host infinitely many minimal tori, bifurcating from a 2-torus orbit.
problem Minimal tori in ellipsoids.
method Analyzing 3D ellipsoids invariant under a 2-torus action.
result Infinitely many distinct minimal tori bifurcate from a 2-torus orbit.
We associate to a parametrized family of nonlinear Fredholm maps possessing a trivial branch of zeroes an {\it index of bifurcation} which provides an algebraic measure for the number of bifurcation points from the trivial branch. The index is derived from the index bundle of the linearization of the …
New bifurcation found in perturbations of non-generic closed self-shrinkers.
problem Understanding the behavior of perturbations in non-generic closed self-shrinkers.
method Analyzing the mean curvature flow singularity transitions.
result Different types of singularity transitions based on perturbation direction.
Study describes bifurcations and solutions of a specific equation on a particular manifold.
problem Analyzing bifurcations and solutions of the vacuum Lichnerowicz equation.
method Exhaustive description of bifurcations and solutions on with invariant seed data.
result Description of CMC slicings of Schwarzschild-de Sitter and Nariai solutions.
Study describes bifurcations of gradient flows on 2-sphere with holes.
problem Analyzing gradient flows on a 2-sphere with up to six singular points.
method Using separatrix diagrams to specify saddle-node and saddle connections.
result Identified all possible topological structures of bifurcations.
Study shows bifurcation in optimal retirement planning.
problem Optimal consumption and retirement planning model.
method Cobb-Douglas utility, simple model with wealth bifurcation.
result Critical wealth level leads to a continuum of retirement trajectories.
New theory shows how membranes can break symmetry.
problem Understanding symmetry breaking in membranes with boundaries.
method Applied bifurcation theory and reduced membrane equation.
result Existence of symmetry breaking bifurcation in membrane solutions.
The paper finds infinitely many metrics with constant sixth order Q-curvature on spheres and related manifolds.
problem Finding constant sixth order Q-curvature metrics on spheres and related manifolds.
method Classical bifurcation technique and Riemannian covering.
result Infinitely many constant sixth order Q-curvature metrics on spheres and related manifolds.
New solutions found for Ginzburg-Landau equations on complex manifolds.
problem Finding solutions to Ginzburg-Landau equations on closed manifolds.
method Bifurcation theory applied to Laplace-type operator eigenvalues.
result First nonminimal and irreducible solutions on nontrivial line bundles.
We obtain an estimate for the covering dimension of the set of bifurcation points for solutions of nonlinear elliptic boundary value problems from the principal symbol of the linearization of the problem along the trivial branch of solutions.
Study detects P-type bifurcations in single system realizations using unreliable kernel density estimates.
problem Detecting P-type bifurcations in signals with unreliable kernel density estimates.
method Create persistence diagrams from single system realization, statistically analyze resulting set, compare point process modeling methods.
result Subsampling outperforms other point process modeling methods in predicting P-type bifurcations.
Trans-Bifurcation Prediction of Dynamics in terms of Extreme Learning Machines with Control Inputsnlin.CD
Extremely accurate prediction of dynamical system bifurcations using control inputs.
problem Predicting complex bifurcation structures in dynamical systems.
method Extending extreme learning machines with control inputs to model system dynamics.
result The model can nearly reproduce the entire structure of bifurcations using only a few parameter values.
Study bifurcations of curves on surfaces in Minkowski 3-space.
problem Understanding the behavior of curves on surfaces in Minkowski 3-space.
method Analyzing the degeneracy of induced pseudo metric, discriminant of principal curvatures, parabolic curve, and mean curvature vanishing points.
result Bifurcations of robust features on surfaces in Minkowski 3-space.
Study finds multiple constant curvature metrics in product spaces.
problem Finding multiple constant scalar curvature metrics in product spaces.
method Equivariant bifurcation theory.
result Multiplicity of constant scalar curvature metrics discovered.
Criteria for Morin singularities in lower dimensions with applications to bifurcation.
problem Understanding Morin singularities in maps into lower dimensions.
method Providing criteria for Morin singularities and studying bifurcations of Lefschetz singularities.
result Criteria for Morin singularities in maps into lower dimensions.
We extend the notion of reticular Legendrian unfoldings in order to investigate multi-time bifurcations of wavefronts generated by an r-corner. We give a classification list of generic and stable bifurcations with two time parameter and give all generic figures in the plane and the space.
The paper finds multiple solutions to the Yamabe problem on specific product manifolds.
problem Finding multiple solutions to the Yamabe problem on product manifolds with minimal boundary.
method Using bifurcation theory to analyze solutions.
result Multiple solutions to the Yamabe problem are identified.
The paper determines the bifurcation set of a real polynomial function of two variables using Newton polygons.
problem Determining the bifurcation set of a real polynomial function of two variables.
method Using toric compactification and toric modifications to count singular phenomena at infinity.
result An upper bound of the number of elements in the bifurcation set is given in terms of its Newton polygon.
Deep learning detects bifurcations in dynamical systems.
problem Predicting catastrophic changes in dynamical systems across sciences.
method Data-driven, physically-informed deep-learning framework for classifying dynamical regimes and characterizing bifurcation boundaries.
result Extracts topologically invariant features to detect bifurcation boundaries in unseen systems.
Euler-Plateau, with a twistcond-mat.soft
A generalization of the Euler-Plateau problem to account for the energy contribution due to twisting of the bounding loop is proposed. Euler-Lagrange equations are derived in a parameterized setting and a bifurcation analysis is performed. A pair of dimensionless parameters govern bifurcations from a flat, circular gro…
Paper uses Simulated Bifurcation for quick asset allocation optimization.
problem Optimal asset allocation selection.
method Simulated Bifurcation algorithms applied to 441 S&P500 assets.
result Unrivaled timescale for optimal sub-allocation selection.
We study bifurcation from a branch of trivial solutions of semilinear elliptic Dirichlet boundary value problems on a geodesic ball, whose radius is used as the bifurcation parameter. In the proof of our main theorem we obtain in addition a special case of an index theorem due to S. Smale.
We give two numerical methods for computing the first bifurcation point for Delaunay nodoids. With regard to methods for constructing constant mean curvature surfaces, we conclude that the bifurcation point in the analytic method of Mazzeo-Pacard is the same as a limiting point encountered in the integrable systems met…
The paper explains how the conjugate locus of a point on a surface can gain or lose cusps as the point moves.
problem Understanding the behavior of the conjugate locus as a point moves on a surface.
method Explains bifurcations in terms of vanishing higher derivatives of the exponential map and classifies them using scalar invariants.
result Simple equations for higher derivatives of the exponential map are derived, and the bifurcations of cusps are classified based on the local structure of the conjugate locus.