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### A Condition for a Polynomial Map to be Invertible.

Mathematische Annalen

### A continuation method for motion-planning problems

ESAIM: Control, Optimisation and Calculus of Variations

We apply the well-known homotopy continuation method to address the motion planning problem (MPP) for smooth driftless control-affine systems. The homotopy continuation method is a Newton-type procedure to effectively determine functions only defined implicitly. That approach requires first to characterize the singularities of a surjective map and next to prove global existence for the solution of an ordinary differential equation, the Wazewski equation. In the context of the MPP, the aforementioned...

### A continuation method for motion-planning problems

ESAIM: Control, Optimisation and Calculus of Variations

We apply the well-known homotopy continuation method to address the motion planning problem (MPP) for smooth driftless control-affine systems. The homotopy continuation method is a Newton-type procedure to effectively determine functions only defined implicitly. That approach requires first to characterize the singularities of a surjective map and next to prove global existence for the solution of an ordinary differential equation, the Wazewski equation. In the context of the MPP, the aforementioned...

### A generalization of the interior mapping theorem of Clarke and Pourciau

Commentationes Mathematicae Universitatis Carolinae

### A global analysis of Newton iterations for determining turning points

Applications of Mathematics

The global convergence of a direct method for determining turning (limit) points of a parameter-dependent mapping is analysed. It is assumed that the relevant extended system has a singular root for a special parameter value. The singular root is clasified as a $bifurcationsingularity$ (i.e., as a $degenerate$ turning point). Then, the Theorz for Imperfect Bifurcation offers a particular scenario for the split of the singular root into a finite number of regular roots (turning points) due to a given parameter imperfection. The relationship...

### A note on the inverse function theorem of Nash and Moser.

International Journal of Mathematics and Mathematical Sciences

### A proof of the inverse function theorem

Revista colombiana de matematicas

### A remark on small divisors problems

Czechoslovak Mathematical Journal

### An application of the induction method of V. Pták to the study of regula falsi

Aplikace matematiky

In this paper we introduce the notion of "$p$-dimensional rate of convergence" which generalizes the notion of rate of convergence introduced by V. Pták. Using this notion we give a generalization of the Induction Theorem of V. Pták, which may constitute a basis for the study of the iterative procedures of the form ${X}_{n+1}=F\left({x}_{n-p+1},{X}_{n-p+2},...,{x}_{n}\right)$, $n=0,1,2,...$. As an illustration we apply these results to the study of the convergence of the secant method, obtaining sharp estimates for the errors at each step of the iterative procedure.

### An application of the Nash-Moser theorem to ordinary differential equations in Fréchet spaces

Studia Mathematica

A general existence and uniqueness result of Picard-Lindelöf type is proved for ordinary differential equations in Fréchet spaces as an application of a generalized Nash-Moser implicit function theorem. Many examples show that the assumptions of the main result are natural. Applications are given for the Fréchet spaces ${C}^{\infty }\left(K\right)$, $S\left({ℝ}^{N}\right)$, $B\left(ℝ{R}^{N}\right)$, ${D}_{{L}_{1}}\left({ℝ}^{N}\right)$, for Köthe sequence spaces, and for the general class of subbinomic Fréchet algebras.

### An Effective Approach to Keller's Jacobian Conjecture.

Mathematische Annalen

### An implicit function theorem in Banach spaces

Annales Polonici Mathematici

### An inverse function theorem for Frechet spaces

Banach Center Publications

### An inverse function theorem in Fréchet spaces without smoothing operators

Annales Polonici Mathematici

### Approximations of continuous Newton's method: an extension of Cayley's problem.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### Arithmetic Monodromy Groups.

Mathematische Annalen

### Concerning interior mapping theorem

Commentationes Mathematicae Universitatis Carolinae

### Differentiable manifolds with generalized boundary

Czechoslovak Mathematical Journal

### Existence of Metrics With Prescribed Ricci Curvature: Local Theory.

Inventiones mathematicae

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